Catenary Anchor Leg Mooring System (CALM) is one of the main components of an offshore transport terminal, in which its buoyancy is connected by multiple anchor chains fixed on the sea bed. Since the anchor chain is characterized with a large deformation, it is prone to fatigue failure under dynamic loads in marine environments. These factors lead to many challenges in the design optimization of the anchor chains. The paper is to develop a rapid optimization design frame work for the mooring anchor chain with a minimum cost as the design objective. In the frame work, an approximation model of the mooring analysis is built based on an adaptive sampling method, and a combination of genetic algorithm and sequential quadratic programming method are utilized to optimize the established approximation model. The results show that the frame work greatly reduces the computation time, and the error of the final optimization result obtained by the adaptive sampling is significantly reduced. Compared with other functions, it is found to be better to use the quadratic function as the adaptive function to obtain the optimization result.