Identifying the emotional state from speech is essential for the natural interaction of the machine with the speaker. However, extracting effective features for emotion recognition is difficult, as emotions are ambiguous. We propose a novel approach to learn discriminative features from variable length spectrograms for emotion recognition by cooperating softmax cross-entropy loss and center loss together. The softmax cross-entropy loss enables features from different emotion categories separable, and center loss efficiently pulls the features belonging to the same emotion category to their center. By combining the two losses together, the discriminative power will be highly enhanced, which leads to network learning more effective features for emotion recognition. As demonstrated by the experimental results, after introducing center loss, both the unweighted accuracy and weighted accuracy are improved by over 3\% on Mel-spectrogram input, and more than 4\% on Short Time Fourier Transform spectrogram input.