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 multimodality problem: the target words may come from multiple feasible translations. To address this problem, we propose a novel NAT framework ReorderNAT which explicitly models the reordering information to guide the decoding of NAT. Specially, ReorderNAT utilizes deterministic and non-deterministic decoding strategies that leverage reordering information as a proxy for the final translation to encourage the decoder to choose words belonging to the same translation. Experimental results on various widely-used datasets show that our proposed model achieves better performance compared to most existing NAT models, and even achieves comparable translation quality as autoregressive translation models with a significant speedup.