diff --git a/core/src/main/java/org/apache/calcite/runtime/SqlFunctions.java b/core/src/main/java/org/apache/calcite/runtime/SqlFunctions.java
index 650403098b07..d966cc0f0dc4 100644
--- a/core/src/main/java/org/apache/calcite/runtime/SqlFunctions.java
+++ b/core/src/main/java/org/apache/calcite/runtime/SqlFunctions.java
@@ -879,6 +879,22 @@ public static String translateWithCharset(String s, String transcodingName) {
   }
 
   /** SQL {@code PARSE_URL(urlStr, partToExtract [, keyToExtract] )} function. */
+  public static @Nullable String parseUrl(@Nullable String urlStr,
+      @Nullable String partToExtract, @Nullable String keyToExtract) {
+    if (partToExtract == null || !partToExtract.equals("QUERY")) {
+      return null;
+    }
+
+    String query = parseUrl(urlStr, partToExtract);
+    if (query == null) {
+      return null;
+    }
+
+    Pattern p = Pattern.compile("(&|^)" + keyToExtract + "=([^&]*)");
+    Matcher m = p.matcher(query);
+    return m.find() ? m.group(2) : null;
+  }
+
   public static @Nullable String parseUrl(@Nullable String urlStr,
       @Nullable String partToExtract) {
     if (urlStr == null || partToExtract == null) {
@@ -930,30 +946,12 @@ public static String translateWithCharset(String s, String transcodingName) {
       extractValue = uri.getRawUserInfo();
       break;
     default:
-      return null;
+      extractValue = null;
+      break;
     }
     return extractValue;
   }
 
-  public static @Nullable String parseUrl(@Nullable String urlStr,
-      @Nullable String partToExtract, @Nullable String keyToExtract) {
-    if (partToExtract == null || !partToExtract.equals("QUERY")) {
-      return null;
-    }
-
-    String query = parseUrl(urlStr, partToExtract);
-    if (query == null) {
-      return null;
-    }
-
-    Pattern p = Pattern.compile("(&|^)" + keyToExtract + "=([^&]*)");
-    Matcher m = p.matcher(query);
-    if (m.find()) {
-      return m.group(2);
-    }
-    return null;
-  }
-
   /** SQL {@code RTRIM} function applied to string. */
   public static String rtrim(String s) {
     return trim(false, true, " ", s);
diff --git a/site/_docs/reference.md b/site/_docs/reference.md
index 2d4df4bb7c5e..e1a8d39fc9fd 100644
--- a/site/_docs/reference.md
+++ b/site/_docs/reference.md
@@ -2769,7 +2769,7 @@ BigQuery's type system uses confusingly different names for types and functions:
 | b | PARSE_DATETIME(format, string)                 | Uses format specified by *format* to convert *string* representation of datetime to a TIMESTAMP value
 | b | PARSE_TIME(format, string)                     | Uses format specified by *format* to convert *string* representation of time to a TIME value
 | b | PARSE_TIMESTAMP(format, string[, timeZone])    | Uses format specified by *format* to convert *string* representation of timestamp to a TIMESTAMP WITH LOCAL TIME ZONE value in *timeZone*
-| h s | PARSE_URL(urlString, partToExtract [, keyToExtract] ) | Returns the specified part from the *urlString*. Valid values for *partToExtract* include HOST, PATH, QUERY, REF, PROTOCOL, AUTHORITY, FILE, and USERINFO
+| h s | PARSE_URL(urlString, partToExtract [, keyToExtract] ) | Returns the specified part from the *urlString*. Valid values for *partToExtract* include HOST, PATH, QUERY, REF, PROTOCOL, AUTHORITY, FILE, and USERINFO. *keyToExtract* specifies which query to extract
 | b | POW(numeric1, numeric2)                        | Returns *numeric1* raised to the power *numeric2*
 | m o | REGEXP_REPLACE(string, regexp, rep [, pos [, occurrence [, matchType]]]) | Replaces all substrings of *string* that match *regexp* with *rep* at the starting *pos* in expr (if omitted, the default is 1), *occurrence* means which occurrence of a match to search for (if omitted, the default is 1), *matchType* specifies how to perform matching
 | b m p | REPEAT(string, integer)                    | Returns a string consisting of *string* repeated of *integer* times; returns an empty string if *integer* is less than 1
diff --git a/testkit/src/main/java/org/apache/calcite/test/SqlOperatorTest.java b/testkit/src/main/java/org/apache/calcite/test/SqlOperatorTest.java
index d3a9d10afc65..30e094d9cf8c 100644
--- a/testkit/src/main/java/org/apache/calcite/test/SqlOperatorTest.java
+++ b/testkit/src/main/java/org/apache/calcite/test/SqlOperatorTest.java
@@ -4013,7 +4013,17 @@ static void checkRlikeFails(SqlOperatorFixture f) {
 
       // test with invalid partToExtract
       f.checkNull("parse_url('http://calcite.apache.org/path1/p.php?k1=v1&k2=v2#Ref1',"
-              + " 'INVALID_PART_TO_EXTRACT')");
+          + " 'INVALID_PART_TO_EXTRACT')");
+      f.checkNull("parse_url('http://calcite.apache.org/path1/p.php?k1=v1&k2=v2#Ref1',"
+          + " 'HOST', 'k1')");
+
+      // test with invalid urlString
+      f.checkNull("parse_url('http:calcite.apache.org/path1/p.php?k1=v1&k2=v2#Ref1',"
+          + " 'HOST')");
+      f.checkNull("parse_url('calcite.apache.org/path1/p.php?k1=v1&k2=v2#Ref1',"
+          + " 'HOST')");
+      f.checkNull("parse_url('/path1/p.php?k1=v1&k2=v2#Ref1',"
+          + " 'HOST')");
 
       // test with operands with null values
       f.checkNull("parse_url('http://calcite.apache.org/path1/p.php?k1=v1&k2=v2#Ref1',"