diff --git a/sklearn/cross_decomposition/pls_.py b/sklearn/cross_decomposition/pls_.py
index 4d77bc2b3249c..c7a53d860ad28 100644
--- a/sklearn/cross_decomposition/pls_.py
+++ b/sklearn/cross_decomposition/pls_.py
@@ -53,6 +53,8 @@ def _nipals_twoblocks_inner_loop(X, Y, mode="A", max_iter=500, tol=1e-06,
         else:  # mode A
             # Mode A regress each X column on y_score
             x_weights = np.dot(X.T, y_score) / np.dot(y_score.T, y_score)
+        if np.dot(x_weights.T, x_weights) < eps:
+            x_weights += eps
         # 1.2 Normalize u
         x_weights /= np.sqrt(np.dot(x_weights.T, x_weights)) + eps
         # 1.3 Update x_score: the X latent scores