diff --git a/mllib/src/main/scala/org/apache/spark/ml/regression/GeneralizedLinearRegression.scala b/mllib/src/main/scala/org/apache/spark/ml/regression/GeneralizedLinearRegression.scala
index 1938e8ecc5..1d2961e027 100644
--- a/mllib/src/main/scala/org/apache/spark/ml/regression/GeneralizedLinearRegression.scala
+++ b/mllib/src/main/scala/org/apache/spark/ml/regression/GeneralizedLinearRegression.scala
@@ -501,8 +501,8 @@ object GeneralizedLinearRegression extends DefaultParamsReadable[GeneralizedLine
     val defaultLink: Link = Log
 
     override def initialize(y: Double, weight: Double): Double = {
-      require(y > 0.0, "The response variable of Poisson family " +
-        s"should be positive, but got $y")
+      require(y >= 0.0, "The response variable of Poisson family " +
+        s"should be non-negative, but got $y")
       y
     }
 
diff --git a/mllib/src/test/scala/org/apache/spark/ml/regression/GeneralizedLinearRegressionSuite.scala b/mllib/src/test/scala/org/apache/spark/ml/regression/GeneralizedLinearRegressionSuite.scala
index 111bc97464..6a4ac1735b 100644
--- a/mllib/src/test/scala/org/apache/spark/ml/regression/GeneralizedLinearRegressionSuite.scala
+++ b/mllib/src/test/scala/org/apache/spark/ml/regression/GeneralizedLinearRegressionSuite.scala
@@ -44,6 +44,7 @@ class GeneralizedLinearRegressionSuite
   @transient var datasetGaussianInverse: DataFrame = _
   @transient var datasetBinomial: DataFrame = _
   @transient var datasetPoissonLog: DataFrame = _
+  @transient var datasetPoissonLogWithZero: DataFrame = _
   @transient var datasetPoissonIdentity: DataFrame = _
   @transient var datasetPoissonSqrt: DataFrame = _
   @transient var datasetGammaInverse: DataFrame = _
@@ -88,6 +89,12 @@ class GeneralizedLinearRegressionSuite
       xVariance = Array(0.7, 1.2), nPoints = 10000, seed, noiseLevel = 0.01,
       family = "poisson", link = "log").toDF()
 
+    datasetPoissonLogWithZero = generateGeneralizedLinearRegressionInput(
+      intercept = -1.5, coefficients = Array(0.22, 0.06), xMean = Array(2.9, 10.5),
+      xVariance = Array(0.7, 1.2), nPoints = 100, seed, noiseLevel = 0.01,
+      family = "poisson", link = "log")
+      .map{x => LabeledPoint(if (x.label < 0.7) 0.0 else x.label, x.features)}.toDF()
+
     datasetPoissonIdentity = generateGeneralizedLinearRegressionInput(
       intercept = 2.5, coefficients = Array(2.2, 0.6), xMean = Array(2.9, 10.5),
       xVariance = Array(0.7, 1.2), nPoints = 10000, seed, noiseLevel = 0.01,
@@ -139,6 +146,10 @@ class GeneralizedLinearRegressionSuite
       label + "," + features.toArray.mkString(",")
     }.repartition(1).saveAsTextFile(
       "target/tmp/GeneralizedLinearRegressionSuite/datasetPoissonLog")
+    datasetPoissonLogWithZero.rdd.map { case Row(label: Double, features: Vector) =>
+      label + "," + features.toArray.mkString(",")
+    }.repartition(1).saveAsTextFile(
+      "target/tmp/GeneralizedLinearRegressionSuite/datasetPoissonLogWithZero")
     datasetPoissonIdentity.rdd.map { case Row(label: Double, features: Vector) =>
       label + "," + features.toArray.mkString(",")
     }.repartition(1).saveAsTextFile(
@@ -456,6 +467,40 @@ class GeneralizedLinearRegressionSuite
     }
   }
 
+  test("generalized linear regression: poisson family against glm (with zero values)") {
+    /*
+       R code:
+       f1 <- data$V1 ~ data$V2 + data$V3 - 1
+       f2 <- data$V1 ~ data$V2 + data$V3
+
+       data <- read.csv("path", header=FALSE)
+       for (formula in c(f1, f2)) {
+         model <- glm(formula, family="poisson", data=data)
+         print(as.vector(coef(model)))
+       }
+       [1]  0.4272661 -0.1565423
+       [1] -3.6911354  0.6214301  0.1295814
+     */
+    val expected = Seq(
+      Vectors.dense(0.0, 0.4272661, -0.1565423),
+      Vectors.dense(-3.6911354, 0.6214301, 0.1295814))
+
+    import GeneralizedLinearRegression._
+
+    var idx = 0
+    val link = "log"
+    val dataset = datasetPoissonLogWithZero
+    for (fitIntercept <- Seq(false, true)) {
+      val trainer = new GeneralizedLinearRegression().setFamily("poisson").setLink(link)
+        .setFitIntercept(fitIntercept).setLinkPredictionCol("linkPrediction")
+      val model = trainer.fit(dataset)
+      val actual = Vectors.dense(model.intercept, model.coefficients(0), model.coefficients(1))
+      assert(actual ~= expected(idx) absTol 1e-4, "Model mismatch: GLM with poisson family, " +
+        s"$link link and fitIntercept = $fitIntercept (with zero values).")
+      idx += 1
+    }
+  }
+
   test("generalized linear regression: gamma family against glm") {
     /*
        R code: