Consistency models have exhibited remarkable capabilities in facilitating efficient image/video generation, enabling synthesis with minimal sampling steps. It has proven to be advantageous in mitigating the computational burdens associated with diffusion models. Nevertheless, the application of consistency models in music generation remains largely unexplored. To address this gap, we present Music Consistency Models (\texttt{MusicCM}), which leverages the concept of consistency models to efficiently synthesize mel-spectrogram for music clips, maintaining high quality while minimizing the number of sampling steps. Building upon existing text-to-music diffusion models, the \texttt{MusicCM} model incorporates consistency distillation and adversarial discriminator training. Moreover, we find it beneficial to generate extended coherent music by incorporating multiple diffusion processes with shared constraints. Experimental results reveal the effectiveness of our model in terms of computational efficiency, fidelity, and naturalness. Notable, \texttt{MusicCM} achieves seamless music synthesis with a mere four sampling steps, e.g., only one second per minute of the music clip, showcasing the potential for real-time application.