Audio super-resolution is a challenging task of recovering the missing high-resolution features from a low-resolution signal. To address this, generative adversarial networks (GAN) have been used to achieve promising results by training the mappings between magnitudes of the low and high-frequency components. However, phase information is not well-considered for waveform reconstruction in conventional methods. In this paper, we tackle the problem of music super-resolution and conduct a thorough investigation on the importance of phase for this task. We use GAN to predict the magnitudes of the high-frequency components. The corresponding phase information can be extracted using either a GAN-based waveform synthesis system or a modified Griffin-Lim algorithm. Experimental results show that phase information plays an important role in the improvement of the reconstructed music quality. Moreover, our proposed method significantly outperforms other state-of-the-art methods in terms of objective evaluations.