Generative Adversarial Network (GAN) has been proposed to tackle the exposure bias problem of Neural Machine Translation (NMT). However, the discriminator typically results in the instability of the GAN training due to the inadequate training problem: the search space is so huge that sampled translations are not sufficient for discriminator training. To address this issue and stabilize the GAN training, in this paper, we propose a novel Bidirectional Generative Adversarial Network for Neural Machine Translation (BGAN-NMT), which aims to introduce a generator model to act as the discriminator, whereby the discriminator naturally considers the entire translation space so that the inadequate training problem can be alleviated. To satisfy this property, generator and discriminator are both designed to model the joint probability of sentence pairs, with the difference that, the generator decomposes the joint probability with a source language model and a source-to-target translation model, while the discriminator is formulated as a target language model and a target-to-source translation model. To further leverage the symmetry of them, an auxiliary GAN is introduced and adopts generator and discriminator models of original one as its own discriminator and generator respectively. Two GANs are alternately trained to update the parameters. Experiment results on German-English and Chinese-English translation tasks demonstrate that our method not only stabilizes GAN training but also achieves significant improvements over baseline systems.