Non-autoregressive neural machine translation (NAT) generates each target word in parallel and has achieved promising inference acceleration. However, existing NAT models still have a big gap in translation quality compared to autoregressive neural machine translation models due to the enormous decoding space. To address this problem, we propose a novel NAT framework named ReorderNAT which explicitly models the reordering information in the decoding procedure. We further introduce deterministic and non-deterministic decoding strategies that utilize reordering information to narrow the decoding search space in our proposed ReorderNAT. Experimental results on various widely-used datasets show that our proposed model achieves better performance compared to existing NAT models, and even achieves comparable translation quality as autoregressive translation models with a significant speedup.