Through kinematic analysis of the H shaped parallel mechanism, the degree of freedom was derived. The inverse and forward position model of this mechanism were established by employing kinematic superposition principle and the analytical solution was obtained. The condition number of Jacobian matrix was derived and the workspace was analysed. The result of the calculation shows that this mechanism had perfect isotropic properties and specious workspace. Further analysis of the inverse position solution adopting homogeneous transformation and matrix decomposition indicated that the trajectory between the input and output coordinate was geometrically similar. Based on that, a control strategy for fine interpolation only using general motion controller was proposed. A model machine was developed and a series of experiments were carried out, such as line/circle interpolation, continuous interpolation and etc. The results suggest that the mathematical model established for this parallel mechanism was correct.