The false data injection attack is a typical cyber attack method which seriously endangers the security of power systems. Most studies of false data injection attacks regard it as a one-shot event, including the researches on the development of attack methods. However, this cannot fully demonstrate the threats of false data injection attacks. Therefore, this paper takes the dynamic behavior of the false data injection attack into account and addresses the constrains of attack resources and operations in practice. Then based on the optimal control theory, an optimal dynamic attack strategy is proposed, which significantly improves the attack effect on limited energy conditions, and reduces the possibility of being detected to a certain extent. When some conditions permit, it can be reinforced with other stealth attack methods to completely bypass the detection.