diff --git a/src/data/data.cc b/src/data/data.cc
index 2d5996331..f99d3368e 100644
--- a/src/data/data.cc
+++ b/src/data/data.cc
@@ -898,11 +898,12 @@ uint64_t SparsePage::Push(const AdapterBatchT& batch, float missing, int nthread
     return max_columns;
   }
   std::vector<std::vector<uint64_t>> max_columns_vector(nthread);
-  dmlc::OMPException exc;
+  dmlc::OMPException exec;
+  std::atomic<bool> valid{true};
   // First-pass over the batch counting valid elements
 #pragma omp parallel num_threads(nthread)
   {
-    exc.Run([&]() {
+    exec.Run([&]() {
       int tid = omp_get_thread_num();
       size_t begin = tid*thread_size;
       size_t end = tid != (nthread-1) ? (tid+1)*thread_size : batch_size;
@@ -912,7 +913,10 @@ uint64_t SparsePage::Push(const AdapterBatchT& batch, float missing, int nthread
       for (size_t i = begin; i < end; ++i) {
         auto line = batch.GetLine(i);
         for (auto j = 0ull; j < line.Size(); j++) {
-          auto element = line.GetElement(j);
+          data::COOTuple const& element = line.GetElement(j);
+          if (!std::isinf(missing) && std::isinf(element.value)) {
+            valid = false;
+          }
           const size_t key = element.row_idx - base_rowid;
           CHECK_GE(key,  builder_base_row_offset);
           max_columns_local =
@@ -927,7 +931,8 @@ uint64_t SparsePage::Push(const AdapterBatchT& batch, float missing, int nthread
       }
     });
   }
-  exc.Rethrow();
+  exec.Rethrow();
+  CHECK(valid) << "Input data contains `inf` or `nan`";
   for (const auto & max : max_columns_vector) {
     max_columns = std::max(max_columns, max[0]);
   }
@@ -938,7 +943,7 @@ uint64_t SparsePage::Push(const AdapterBatchT& batch, float missing, int nthread
 
 #pragma omp parallel num_threads(nthread)
   {
-    exc.Run([&]() {
+    exec.Run([&]() {
       int tid = omp_get_thread_num();
       size_t begin = tid*thread_size;
       size_t end = tid != (nthread-1) ? (tid+1)*thread_size : batch_size;
@@ -954,7 +959,7 @@ uint64_t SparsePage::Push(const AdapterBatchT& batch, float missing, int nthread
       }
     });
   }
-  exc.Rethrow();
+  exec.Rethrow();
   omp_set_num_threads(nthread_original);
 
   return max_columns;
diff --git a/tests/cpp/data/test_simple_dmatrix.cc b/tests/cpp/data/test_simple_dmatrix.cc
index 3147395a6..f777b00e2 100644
--- a/tests/cpp/data/test_simple_dmatrix.cc
+++ b/tests/cpp/data/test_simple_dmatrix.cc
@@ -116,6 +116,14 @@ TEST(SimpleDMatrix, MissingData) {
   CHECK_EQ(dmat->Info().num_nonzero_, 2);
   dmat.reset(new data::SimpleDMatrix(&adapter, 1.0, 1));
   CHECK_EQ(dmat->Info().num_nonzero_, 1);
+
+  {
+    data[1] = std::numeric_limits<float>::infinity();
+    data::DenseAdapter adapter(data.data(), data.size(), 1);
+    EXPECT_THROW(data::SimpleDMatrix dmat(
+                     &adapter, std::numeric_limits<float>::quiet_NaN(), -1),
+                 dmlc::Error);
+  }
 }
 
 TEST(SimpleDMatrix, EmptyRow) {