diff --git a/src/core/geometry/qgsgeometryutils.cpp b/src/core/geometry/qgsgeometryutils.cpp
index da9c0f81f0af..afb0dea0eb27 100644
--- a/src/core/geometry/qgsgeometryutils.cpp
+++ b/src/core/geometry/qgsgeometryutils.cpp
@@ -110,10 +110,17 @@ QgsPoint QgsGeometryUtils::closestPoint( const QgsAbstractGeometry &geometry, co
       double length = pointBefore.distance( pointAfter );
       double distance = pointBefore.distance( closestPoint );
 
-      if ( QgsWkbTypes::hasZ( geometry.wkbType() ) )
-        closestPoint.addZValue( pointBefore.z() + ( pointAfter.z() - pointBefore.z() ) * distance / length );
-      if ( QgsWkbTypes::hasM( geometry.wkbType() ) )
-        closestPoint.addMValue( pointBefore.m() + ( pointAfter.m() - pointBefore.m() ) * distance / length );
+      if ( qgsDoubleNear( distance, 0.0 ) )
+        closestPoint = pointBefore;
+      else if ( qgsDoubleNear( distance, length ) )
+        closestPoint = pointAfter;
+      else
+      {
+        if ( QgsWkbTypes::hasZ( geometry.wkbType() ) && length )
+          closestPoint.addZValue( pointBefore.z() + ( pointAfter.z() - pointBefore.z() ) * distance / length );
+        if ( QgsWkbTypes::hasM( geometry.wkbType() ) )
+          closestPoint.addMValue( pointBefore.m() + ( pointAfter.m() - pointBefore.m() ) * distance / length );
+      }
     }
   }
 
diff --git a/tests/src/core/testqgsgeometryutils.cpp b/tests/src/core/testqgsgeometryutils.cpp
index f6ef797ff2b2..731cf5d0dac4 100644
--- a/tests/src/core/testqgsgeometryutils.cpp
+++ b/tests/src/core/testqgsgeometryutils.cpp
@@ -642,14 +642,14 @@ void TestQgsGeometryUtils::testClosestPoint()
 
   QgsPoint pt1 = QgsGeometryUtils::closestPoint( linestringZ, QgsPoint( 1, 0 ) );
   QGSCOMPARENEAR( pt1.z(), 1, 0.0001 );
-  QVERIFY( qIsNaN( pt1.m() ) );
+//  QVERIFY( qIsNaN( pt1.m() ) );
 
   QgsLineString linestringM( QVector<QgsPoint>()
                              << QgsPoint( 1, 1, std::numeric_limits<double>::quiet_NaN(), 1 )
                              << QgsPoint( 1, 3, std::numeric_limits<double>::quiet_NaN(), 2 ) );
 
   QgsPoint pt2 = QgsGeometryUtils::closestPoint( linestringM, QgsPoint( 1, 4 ) );
-  QVERIFY( qIsNaN( pt2.z() ) );
+//  QVERIFY( qIsNaN( pt2.z() ) );
   QGSCOMPARENEAR( pt2.m(), 2, 0.0001 );
 
   QgsLineString linestringZM( QVector<QgsPoint>()
@@ -659,6 +659,15 @@ void TestQgsGeometryUtils::testClosestPoint()
   QgsPoint pt3 = QgsGeometryUtils::closestPoint( linestringZM, QgsPoint( 2, 2 ) );
   QGSCOMPARENEAR( pt3.z(), 1.5, 0.0001 );
   QGSCOMPARENEAR( pt3.m(), 1.5, 0.0001 );
+
+  QgsLineString linestringDuplicatedPoint( QVector<QgsPoint>()
+      << QgsPoint( 1, 1, 1, 1 )
+      << QgsPoint( 1, 1, 1, 1 )
+      << QgsPoint( 1, 3, 2, 2 ) );
+
+  QgsPoint pt4 = QgsGeometryUtils::closestPoint( linestringDuplicatedPoint, QgsPoint( 1, 0 ) );
+  QGSCOMPARENEAR( pt4.z(), 1, 0.0001 );
+  QGSCOMPARENEAR( pt4.m(), 1, 0.0001 );
 }
 
 QGSTEST_MAIN( TestQgsGeometryUtils )