Non-autoregressive Transformer(NAT) significantly accelerates the inference of neural machine translation. However, conventional NAT models suffer from limited expression power and performance degradation compared to autoregressive (AT) models due to the assumption of conditional independence among target tokens. To address these limitations, we propose a novel approach called PCFG-NAT, which leverages a specially designed Probabilistic Context-Free Grammar (PCFG) to enhance the ability of NAT models to capture complex dependencies among output tokens. Experimental results on major machine translation benchmarks demonstrate that PCFG-NAT further narrows the gap in translation quality between NAT and AT models. Moreover, PCFG-NAT facilitates a deeper understanding of the generated sentences, addressing the lack of satisfactory explainability in neural machine translation. Code is publicly available at https://github.com/ictnlp/PCFG-NAT.