Stiffness and workspace are crucial performance indexes of a precision mechanism. In this paper, an optimization method is presented, for a compliant parallel platform to achieve desired stiffness and workspace. First, a numerical model is proposed to reveal the relationship between structural parameters, desired stiffness and workspace of the compliant parallel platform. Then, the influence of the various parameters on stiffness and workspace of the platform is analyzed. Based on Gaussian distribution, the multi-objective optimization problem is transformed into a single-objective one, in order to guarantee convergence precision. Furthermore, particle swarm optimization is used to optimize the structural parameters of the platform, which significantly improve its stiffness and workspace. Last, the effectiveness of the proposed numerical model is verified by finite element analysis and experiment.