Neural generative models have achieved promising performance on dialog generation tasks if given a huge data set. However, the lack of high-quality dialog data and the expensive data annotation process greatly limit their application in real-world settings. We propose a paraphrase augmented response generation (PARG) framework that jointly trains a paraphrase model and a response generation model to improve the dialog generation performance. We also design a method to automatically construct paraphrase training data set based on dialog state and dialog act labels. PARG is applicable to various dialog generation models, such as TSCP (Lei et al., 2018) and DAMD (Zhang et al., 2019). Experimental results show that the proposed framework improves these state-of-the-art dialog models further on CamRest676 and MultiWOZ. PARG also significantly outperforms other data augmentation methods in dialog generation tasks, especially under low resource settings.