The kinematics of robot wrist refers to the motion information of a manipulator, such as positions, velocities, and accelerations. It is very crucial for analysing the behaviour of robot wrist using a suitable kinematics model with a result of many valuable contributions. However, current researches always focus on full-actuated robot wrist. The proposed underactuated robot wrist is a novel mechanism with small volume, lightweight, low cost, low energy consumption, and high flexibility, thus designing a robot wrist with fewer actuators than the degrees of freedom becomes an important issue. This article is devoted to kinematics analysis model of a novel underactuated robot wrist. After the novel understated robot wrist was introduced, the inverse kinematics analysis and forward kinematic analysis of the underactuated robot wrist with numerical simulation based on virtual prototyping were discussed in detail. The verification of the forward kinematic analysis and inverse kinematics analysis is used to demonstrate the proposed methodology.