The cost of support structures in offshore wind turbines accounts for about a quarter of the total construction cost, and therefore the optimized design of support structures has significant economic benefits. Based on the guide-weight method which is a gradient-based optimization algorithm, a gradual optimization algorithm is proposed to optimize the monopile support structure that is widely used in offshore wind turbines. The optimization variables are defined based on the actual tower and pile sections, and the multi-constraint optimization problem is established by considering the constraints including displacement, natural frequency, strength, and geometric size. The interactions between the support structures and loads of wind, waves and currents are considered through multiple rounds of progressive optimization. The application of automatic differentiation technology makes it possible to efficiently evaluate the sensitivities of constraints under the condition that the constraints are expressed on basis of relative design specifications. Through the optimization of an established case, the proposed method is found to be stable, efficient and effective to reduce the cost of the monopile support structure.