diff --git a/doc/whats_new/v0.20.rst b/doc/whats_new/v0.20.rst
index 6f5636642bccf..6ccdc58b7b3b0 100644
--- a/doc/whats_new/v0.20.rst
+++ b/doc/whats_new/v0.20.rst
@@ -17,6 +17,7 @@ random sampling procedures.
 
 - :class:`decomposition.IncrementalPCA` in Python 2 (bug fix)
 - :class:`isotonic.IsotonicRegression` (bug fix)
+- :class:`metrics.roc_auc_score` (bug fix)
 
 Details are listed in the changelog below.
 
@@ -58,8 +59,6 @@ Classifiers and regressors
   :class:`sklearn.naive_bayes.GaussianNB` to give a precise control over
   variances calculation. :issue:`9681` by :user:`Dmitry Mottl <Mottl>`.
 
-
-
 Model evaluation and meta-estimators
 
 - A scorer based on :func:`metrics.brier_score_loss` is also available.
@@ -108,6 +107,11 @@ Decomposition, manifold learning and clustering
 - Fixed a bug in :func:`datasets.fetch_kddcup99`, where data were not properly
   shuffled. :issue:`9731` by `Nicolas Goix`_.
 
+Metrics
+
+- Fixed a bug due to floating point error in :func:`metrics.roc_auc_score` with
+  non-integer sample weights. :issue:`9786` by :user:`Hanmin Qin <qinhanmin2014>`.
+
 API changes summary
 -------------------
 
diff --git a/sklearn/metrics/ranking.py b/sklearn/metrics/ranking.py
index aa2e5425976e9..435b3b6502f42 100644
--- a/sklearn/metrics/ranking.py
+++ b/sklearn/metrics/ranking.py
@@ -258,7 +258,7 @@ def _binary_roc_auc_score(y_true, y_score, sample_weight=None):
 
         fpr, tpr, tresholds = roc_curve(y_true, y_score,
                                         sample_weight=sample_weight)
-        return auc(fpr, tpr, reorder=True)
+        return auc(fpr, tpr)
 
     return _average_binary_score(
         _binary_roc_auc_score, y_true, y_score, average,
@@ -299,7 +299,7 @@ def _binary_clf_curve(y_true, y_score, pos_label=None, sample_weight=None):
     thresholds : array, shape = [n_thresholds]
         Decreasing score values.
     """
-    check_consistent_length(y_true, y_score)
+    check_consistent_length(y_true, y_score, sample_weight)
     y_true = column_or_1d(y_true)
     y_score = column_or_1d(y_score)
     assert_all_finite(y_true)
@@ -341,7 +341,9 @@ def _binary_clf_curve(y_true, y_score, pos_label=None, sample_weight=None):
     # accumulate the true positives with decreasing threshold
     tps = stable_cumsum(y_true * weight)[threshold_idxs]
     if sample_weight is not None:
-        fps = stable_cumsum(weight)[threshold_idxs] - tps
+        # express fps as a cumsum to ensure fps is increasing even in
+        # the presense of floating point errors
+        fps = stable_cumsum((1 - y_true) * weight)[threshold_idxs]
     else:
         fps = 1 + threshold_idxs - tps
     return fps, tps, y_score[threshold_idxs]
diff --git a/sklearn/metrics/tests/test_common.py b/sklearn/metrics/tests/test_common.py
index 5f775aaf9ac8f..b935ccbe29910 100644
--- a/sklearn/metrics/tests/test_common.py
+++ b/sklearn/metrics/tests/test_common.py
@@ -198,12 +198,6 @@
     "samples_recall_score",
     "coverage_error",
 
-    "roc_auc_score",
-    "micro_roc_auc",
-    "weighted_roc_auc",
-    "macro_roc_auc",
-    "samples_roc_auc",
-
     "average_precision_score",
     "weighted_average_precision_score",
     "micro_average_precision_score",
@@ -218,6 +212,12 @@
 METRIC_UNDEFINED_MULTICLASS = [
     "brier_score_loss",
 
+    "roc_auc_score",
+    "micro_roc_auc",
+    "weighted_roc_auc",
+    "macro_roc_auc",
+    "samples_roc_auc",
+
     # with default average='binary', multiclass is prohibited
     "precision_score",
     "recall_score",
diff --git a/sklearn/metrics/tests/test_ranking.py b/sklearn/metrics/tests/test_ranking.py
index db80691663606..ab8a4684c0c65 100644
--- a/sklearn/metrics/tests/test_ranking.py
+++ b/sklearn/metrics/tests/test_ranking.py
@@ -371,6 +371,18 @@ def test_roc_curve_drop_intermediate():
                               [1.0, 0.9, 0.7, 0.6, 0.])
 
 
+def test_roc_curve_fpr_tpr_increasing():
+    # Ensure that fpr and tpr returned by roc_curve are increasing.
+    # Construct an edge case with float y_score and sample_weight
+    # when some adjacent values of fpr and tpr are actually the same.
+    y_true = [0, 0, 1, 1, 1]
+    y_score = [0.1, 0.7, 0.3, 0.4, 0.5]
+    sample_weight = np.repeat(0.2, 5)
+    fpr, tpr, _ = roc_curve(y_true, y_score, sample_weight=sample_weight)
+    assert_equal((np.diff(fpr) < 0).sum(), 0)
+    assert_equal((np.diff(tpr) < 0).sum(), 0)
+
+
 def test_auc():
     # Test Area Under Curve (AUC) computation
     x = [0, 1]