By installing spring-dampers in the active joints,the multi-dimensional damping platform is set up based on the 3-PCR parallel mechanism. The kinematics equation of the 3-PCR parallel mechanism is derived and the workspace is analyzed. The radii of the upper and lower platforms,the bar length and the angle between the bar and the lower platform are chosen as the optimization variables to investigate their influence on the maximum sphere workspace. The above-mentioned parameters are optimized by genetic algorithm so as to obtain the vibration platform which meets the particular demand of the equivalent stiffness which is nearly constant when the vibration amplitude is small. The equivalent stiffness of vibration reduction platform in engineering application can be realized by using this design method. The presented design process of equivalent stiffness provides a novel approach for the vibration reduction platform design based on parallel mechanism.