Code summarization (CS) and code generation (CG) are two crucial tasks in the field of automatic software development. Various neural network-based approaches are proposed to solve these two tasks separately. However, there exists a specific intuitive correlation between CS and CG, which has not been exploited in previous work. In this paper, we apply the relations between two tasks to improve the performance of both tasks. In other words, exploiting the duality between the two tasks, we propose a dual training framework to train the two tasks simultaneously. In this framework, we consider the dualities on probability and attention weights, and design corresponding regularization terms to constrain the duality. We evaluate our approach on two datasets collected from GitHub, and experimental results show that our dual framework can improve the performance of CS and CG tasks over baselines.