This study proposes a new cosine distance loss function based on the traditional Softmax loss function and Island loss function to guide the learning of deep convolution neural networks and solve the problem of large difference in intra-class expressions and high similarity in inter-class expressions in the facial expression recognition tasks. The proposed method not only reduces the difference of intra-class features in the feature space, but also increases the distribution of inter-class features, thereby improving the effect of feature discrimination. After conducting several experiments and analyses, the accuracy of the facial expression recognition algorithm is observed to be 83.196% based on the RAF-DB facial expression dataset, and the effect is better than those obtained using the Softmax loss function and the Island loss function. Furthermore, the proposed algorithm is highly superior with respect to the facial expression recognition tasks.