As a key actuator for spacecraft orbit control, the thrust performance of a Solid Divert Control Motor (SDCM) directly determines the accuracy of orbit control. The thrust design of SDCMs generally relies on engineering experience. Existing designs can satisfy the prescribed thrust regulation range, but the strong nonlinear relationship between the key parameters of the pintle contour and thrust response is insufficiently considered. Small deviations in these parameters may lead to large deviations in thrust response, limiting the efficiency and accuracy of precise thrust regulation. Therefore, the key geometric parameters of the pintle contour must be refined to linearize the thrust response and achieve accurate thrust matching. To this end, a parametric numerical simulation model of the gas valve of the solid divert control motor was established. Samples of the key pintle contour parameters were generated using an optimal Latin hypercube design, and the thrust responses of each sample at different pintle displacements were calculated. Subsequently, radial basis functions were used to construct rapid prediction models of thrust with respect to the key pintle contour parameters separately at different displacements. On this basis, the key design parameters were iteratively optimized using an inaccurate search strategy, with thrust-output linearity and matching accuracy relative to the target thrust curve defined as the optimization objectives, thereby enabling the reconstruction of the SDCM pintle contour for linear thrust matching. The design results demonstrate that the optimized pintle contour enables a highly linear thrust response with respect to pintle displacement over a regulation range of 2–10 mm, reducing the root mean square error between the designed and required thrust by 96% and thereby validating the effectiveness of the proposed method. The optimization-based design framework developed provides theoretical and methodological support for linear thrust matching and precise thrust regulation.