The compliant vertical access riser (CVAR) is a new riser concept with good compliance; it can significantly reduce operating costs by eliminating the need for additional machines to operate wells directly on the platform. In this study, we determined the optimal riser parameters in terms of the stress and riser weight by optimizing the CVAR, and we compared the optimization results. A two-dimensional nonlinear static CVAR model was deduced according to the principles of virtual work and variation, and the model was verified using MATLAB. Design of experiments and Kriging method were used to reduce the number of sample calculations and improve the modeling accuracy. An appropriate selection of the multi-objective optimization problem (MOP) and the non-dominated sorting genetic algorithm helped to optimize the CVAR design. The non-dominated sorting genetic algorithm II was used to solve the Pareto frontier of the optimization model in order to provide decision makers with more choices for the optimization results. After optimizing the riser parameters, the geometry of the riser was smoother, and the stress and stress differences were greatly reduced; the maximum equivalent stresses at the top and bottom were reduced by 36.6% and 44%, respectively. In addition, the stress difference in the buoyancy block area was reduced by 20.9%, and the weight of the riser was increased significantly by 28.1%.