Despite recent advancement in 3D molecule conformation generation driven by diffusion models, its high computational cost in iterative diffusion/denoising process limits its application. Here, an equivariant consistency model (EC-Conf) was proposed as a fast diffusion method for low-energy conformation generation. In EC-Conf, a modified SE (3)-equivariant transformer model was directly used to encode the Cartesian molecular conformations and a highly efficient consistency diffusion process was carried out to generate molecular conformations. It was demonstrated that, with only one sampling step, it can already achieve comparable quality to other diffusion-based models running with thousands denoising steps. Its performance can be further improved with a few more sampling iterations. The performance of EC-Conf is evaluated on both GEOM-QM9 and GEOM-Drugs sets. Our results demonstrate that the efficiency of EC-Conf for learning the distribution of low energy molecular conformation is at least two magnitudes higher than current SOTA diffusion models and could potentially become a useful tool for conformation generation and sampling. SCIENTIFIC CONTRIBUTIONS: In this work, we proposed an equivariant consistency model that significantly improves the efficiency of conformation generation in diffusion-based models while maintaining high structural quality. This method serves as a general framework and can be further extended to more complex structure generation and prediction tasks, including those involving proteins, in future steps.