Abstract: One of the most common features of unconventional superconducting systems such as heavy fermions，high transition-temperature cuprates and iron pnictides is that the superconductivity emerges in the vicinity of a long-range antiferromagnetically ordered state. In addition to doping charge carriers，the application of external pressure is an effective and clean approach to induce unconventional superconductivity near a magnetic quantum critical point. Here we report on the discovery of superconductivity on the verge of antiferromagnetic order in CrAs via the application of external pressure. Bulk superconductivity with T_c=2 K emerges at the critical pressure P_c=8 kbar，where the first-order antiferromagnetic transition at T_N=265 K under ambient pressure is completely suppressed.The close proximity of superconductivity to an antiferromagnetic order suggests an unconventional pairing mechanism for CrAs. The present finding opens a new avenue in the search for novel superconductors in Cr and other transition metal based systems.