To meet the high-precision and lightweight requirements of a space optical mirror pointing mechanism, a type of space parallel mechanism based on a spherical 5R mechanism was proposed. Load mounting with traditional 5R parallel mechanisms was difficult. To solve this problem, asymmetrical branches and specific linkages were designed. Workspace, dexterity and carrying capacity were used as optimal indices, and structural parameter optimization design was conducted based on performance atlases. Model analysis of the optimized mechanism was conducted by using the finite element method. Optimization results show that the asymmetrical branched-chain mechanism has a better index of dexterity. The barycenter of the pointing mirror load was designed at the center of the spherical mechanism, which makes the mechanism more compact and increases its natural frequency. The proposed parallel pointing mechanism was shown to have good integrated performance. This study provides a basis for high-precision space optical pointing applications.