The driving mechanism of an axisymmetric vectoring exhaust nozzle (AVEN) is a 3-degrees-of-freedom (3-DOF) parallel manipulator (PM) with a centering device. According to the characteristics of the vectoring nozzle’s movement mechanism, the 3-DOF kinematics model of the 3SPS + 3PRS PM is established. The forward and inverse positional posture models are built based on the mechanism architecture of PM and the closed-loop vector method. The Jacobian matrix and Hessian matrix are derived using screw theory, and velocity and acceleration models are established. Based on the principle of virtual work and combined with the kinematics model of PM, a stiffness model was established to analyze stiffness performance. Finally, the effectiveness of the kinematics model of the PM was verified by a simulation, and the variation of stiffness performances with the positional posture of the PM was quantitatively analyzed. The results show that the translational stiffness decreases with forward axial translation of the moving platform and the rotational stiffness is mainly determined by the posture parameters. This study is expected to offer ideas for the kinematic modeling of 3-DOF PM and provide references for application and optimizing of the AVEN’s driving mechanism.