Abstract: In this paper, based on the traditional Lagrange multiplier method, an improved Lagrange multiplier method is proposed to design a class of temporal high-order conservative schemes for the coupled Gross-Pitaevskii equation with the help of optimization strategy. The whole method consists of two parts: 1) the application of a high-order semi-implicit scheme to discretize the original model as a prediction; 2) the utilization of a similar scheme to approximate the optimization model as a correction. Together with appropriate high-order structure-preserving space discretization, the fully discrete scheme has high-order accuracy in time and space, and naturally satisfies the conservation laws of mass and energy of the original model in the discrete sense. Numerical experiments verify the effectiveness of the new method.