Two-dimensional nanomaterials, such as graphene, have been extensively studied because of their outstanding physical properties. Structure and geometry optimization of nanopores on such materials is beneficial for their performances in real-world engineering applications, like water desalination. However, the optimization process often involves very large number of experiments or simulations which are expensive and time-consuming. In this work, we propose a graphene nanopore optimization framework via the combination of deep reinforcement learning (DRL) and convolutional neural network (CNN) for efficient water desalination. The DRL agent controls the growth of nanopore by determining the atom to be removed at each timestep, while the CNN predicts the performance of nanoporus graphene for water desalination: the water flux and ion rejection at a certain external pressure. With the synchronous feedback from CNN-accelerated desalination performance prediction, our DRL agent can optimize the nanoporous graphene efficiently in an online manner. Molecular dynamics (MD) simulations on promising DRL-designed graphene nanopores show that they have higher water flux while maintaining rival ion rejection rate compared to the normal circular nanopores. Semi-oval shape with rough edges geometry of DRL-designed pores is found to be the key factor for their high water desalination performance. Ultimately, this study shows that DRL can be a powerful tool for material design.