This paper proposes an accuracy and efficient solution strategy for analyzing dynamic responses of flexible multibody systems. In the proposed strategy, flexible structures are modeled in the corotational frame, then the discrete mathematical model is solved by an optimized composite method. Due to the introduction of the corotational frame, some advanced linear elements can be directly employed, dramatically decreasing computational costs. For accurately calculating dynamic responses, an optimized three-sub-step composite method is developed wherein algorithmic parameters are optimized for minimizing local truncation errors. The optimized composite method achieves second-order accuracy, unconditional stability, and controllable stability. Some classical flexible dynamic systems are solved in this paper, and numerical results show that compared to the currently popular solution strategy based on the absolute nodal coordinate formulation and the Generalized-α method, under the same computational accuracy, our strategy has great superiorities in efficiency.