This paper describes an efficient method called Riccati discrete time transfer matrix method of multibody system (MS-RDTTMM) for studying the dynamic modeling and anti-swing control design of a two-dimensional overhead crane system, which consists of a trolley, rope, load, and control subsystem. Regarding the rope as a series of rigid segments connected by hinges, a multibody model of the overhead crane system can be developed easily by using MS-RDTTMM. Then three separate fuzzy logic controllers are designed for positioning and anti-swing control. For improving the performance of the predesigned fuzzy control system, the genetic algorithm based on MS-RDTTMM is presented offline to tune the initial control parameters. Using the recursive transfer formula to describe the system dynamics, instead of the global dynamics equation in ordinary dynamics methods, the matrices involved in this method are always very small, and the computational cost of the dynamic analysis and control system optimization can be greatly reduced. The numerical verification is carried out to show the computational efficiency, numerical stability, and control performance of the proposed method.