In this work, we explore the constant-Q transform (CQT) for speech emotion recognition (SER). The CQT-based time-frequency analysis provides variable spectro-temporal resolution with higher frequency resolution at lower frequencies. Since lower-frequency regions of speech signal contain more emotion-related information than higher-frequency regions, the increased low-frequency resolution of CQT makes it more promising for SER than standard short-time Fourier transform (STFT). We present a comparative analysis of short-term acoustic features based on STFT and CQT for SER with deep neural network (DNN) as a back-end classifier. We optimize different parameters for both features. The CQT-based features outperform the STFT-based spectral features for SER experiments. Further experiments with cross-corpora evaluation demonstrate that the CQT-based systems provide better generalization with out-of-domain training data.