This study considers the stochastic analysis of a spherical pendulum, whose bidirectional vibration is reduced by spring and damper installed in the radial direction between the point mass and the cable. Under sway motion, the centrifugal force results in the radial motion, which in its turn produces the Coriolis force to reduce sway motion. In stochastic analysis and design, the problem is that the Monte Carlo simulation is time-consuming, while the full stochastic linearization totally fails to describe the effectiveness of the spring and damper. We propose the partial linearization applied to the Coriolis damping to overcome the disadvantages of two mentioned methods. Moreover, the proposed technique can give the analytical solution of partial linearized system. A numerical simulation is performed to verify the proposed approach.