In this paper, the dynamic stability problem of a parallel wrist mechanism is studied by means of monodromy matrix method. This manipulator adopts a universal joint as the ball-socket mechanism to support the mobile platform and to transmit the motion/torque between the input shaft and the end-effector. The linearized equations of motion of the mechanical system are established to analyze its stability according to the Floquet theory. The instable regions are presented graphically in various parametric charts.