The work aims to propose a RPR/RRPR spherical parallel mechanism, which can be used for inkjet printing and engraving of spherical outer package. The mathematical model of RPR/RRPR spherical parallel mechanism was established. The solutions to forward kinematics and inverse kinematics of the mechanism were analyzed. According to the kinematic analysis, Matlab and SolidWorks were respectively used to draw the reachable workspace of the reference points of the mechanism when its two branched chain supporting rod was under different angles, and the change law of the reachable workspace was analyzed. The results showed that the RPR/RRPR spherical parallel mechanism was in a symmetric reachable workspace, and the area of reachable workspace was increased with the increase in the angle of the two branched chain supporting rod. RPR/RRPR spherical parallel mechanism is used for inkjet printing and engraving of the spherical outer package. The structure is simple and has good working performance and a larger workspace, which can improve the efficiency of inkjet printing and engraving process of the spherical outer package.