To improve the trajectory tracking performance of a spatial rigid-flexible 3-RRRU parallel manipulator, a nonlinear control strategy based on a multibody inverse dynamic solution by means of a transient kinematic correction method was proposed. First, the nonlinear inverse dynamics of a spatial 3-RRRU parallel robot with flexible links was developed according to both the Natural Coordinate Formulation (NCF) and the Absolute Nodal Coordinate Formulation (ANCF). The derived models consider the shear deformation and can describe the large deformation for each beam. By analyzing the compatibility problem during the solution process of the rigid-flexible dynamics of the close-chain mechanism, we were able to develop the transient kinematic correction method and the derived stable causal solutions according to the NCF and the ideal kinematic model. Finally, the control strategy for the manipulator is presented, which was based on the solutions and simulations, and experiments were performed to verify the feasibility and effectiveness of the method. The results showed that the solution precision of the inverse dynamics was 10-6 and that the compatibility error of the constraints was 10-8. Compared with those based on the control strategy of the rigid parallel mechanism, the maximum tracking error and the roundness error of a prescribed circular trajectory based on the provided control strategy can decrease by 0.465 mm and 0.416 mm, respectively. The presented method can solve the compatibility problem of multibody dynamics with constraints, thus effectively improving the overall convergent performance of a dynamic system. The control strategy can provide better tracking performance for the parallel mechanism.