Face recognition remains a challenging task in unconstrained scenarios, especially when faces are partially occluded. To improve the robustness against occlusion, augmenting the training images with artificial occlusions has been proved as a useful approach. However, these artificial occlusions are commonly generated by adding a black rectangle or several object templates including sunglasses, scarfs and phones, which cannot well simulate the realistic occlusions. In this paper, based on the argument that the occlusion essentially damages a group of neurons, we propose a novel and elegant occlusion-simulation method via dropping the activations of a group of neurons in some elaborately selected channel. Specifically, we first employ a spatial regularization to encourage each feature channel to respond to local and different face regions. Then, the locality-aware channel-wise dropout (LCD) is designed to simulate occlusions by dropping out a few feature channels. The proposed LCD can encourage its succeeding layers to minimize the intra-class feature variance caused by occlusions, thus leading to improved robustness against occlusion. In addition, we design an auxiliary spatial attention module by learning a channel-wise attention vector to reweight the feature channels, which improves the contributions of non-occluded regions. Extensive experiments on various benchmarks show that the proposed method outperforms state-of-the-art methods with a remarkable improvement.