Deep reinforcement learning has made significant progress in the field of continuous control, such as physical control and autonomous driving. However, it is challenging for a reinforcement model to learn a policy for each task sequentially due to catastrophic forgetting. Specifically, the model would forget knowledge it learned in the past when trained on a new task. We consider this challenge from two perspectives: i) acquiring task-specific skills is difficult since task information and rewards are not highly related; ii) learning knowledge from previous experience is difficult in continuous control domains. In this paper, we introduce an end-to-end framework namely Continual Diversity Adversarial Network (CDAN). We first develop an unsupervised diversity exploration method to learn task-specific skills using an unsupervised objective. Then, we propose an adversarial self-correction mechanism to learn knowledge by exploiting past experience. The two learning procedures are presumably reciprocal. To evaluate the proposed method, we propose a new continuous reinforcement learning environment named Continual Ant Maze (CAM) and a new metric termed Normalized Shorten Distance (NSD). The experimental results confirm the effectiveness of diversity exploration and self-correction. It is worthwhile noting that our final result outperforms baseline by 18.35% in terms of NSD, and 0.61 according to the average reward.