Audio captioning aims at generating natural language descriptions for audio clips automatically. Existing audio captioning models have shown promising improvement in recent years. However, these models are mostly trained via maximum likelihood estimation (MLE), which tends to make captions generic, simple and deterministic. As different people may describe an audio clip from different aspects using distinct words and grammars, we argue that an audio captioning system should have the ability to generate diverse captions for a fixed audio clip and across similar audio clips. To address this problem, we propose an adversarial training framework for audio captioning based on a conditional generative adversarial network (C-GAN), which aims at improving the naturalness and diversity of generated captions. Unlike processing data of continuous values in a classical GAN, a sentence is composed of discrete tokens and the discrete sampling process is non-differentiable. To address this issue, policy gradient, a reinforcement learning technique, is used to back-propagate the reward to the generator. The results show that our proposed model can generate more diverse captions, as compared to state-of-the-art methods.