Recently, the flexible cryogenic hose has been preferred as an alternative to exploit offshore liquefied natural gas (LNG), in which helical corrugated steel pipe is the crucial component with C-shaped corrugation. Parametric finite element models of the LNG cryogenic helical corrugated pipe are established using a 3D shell element in this paper. Considering the nonlinearity of cryogenic material and large geometric structural deformation, mechanical behaviors are simulated under axial tension, bending, and inner pressure loads. In addition, design parameters are determined to optimize the shape of flexible cryogenic hose structures through sectional dimension analysis, and sensitivity analysis is performed with changing geometric parameters. A multi-objective optimization to minimize stiffness and stress is formulated under operation conditions. Full factorial experiment and radial basis function (RBF) neural network are applied to establish the approximated model for structure analysis. The Pareto optimal solution set and value range of parameters are obtained through NSGA-II GA algorithm under manufacturing and stiffness constraints, thereby providing a feasible optimal approach for the structural design of LNG cryogenic corrugated hose.