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. In this way, the activations affected by an occlusion in a local region are more likely to be located in a single feature channel. Then, the locality-aware channel-wise dropout (LCD) is designed to simulate the occlusion by dropping out the entire feature channel. Furthermore, by randomly dropping out several feature channels, our method can well simulate the occlusion of larger area. 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.