Due to the requirement of multi-dimensional nanometer level positioning of the compliant precision mechanism, a piezo-driven spatial compliant parallel mechanism was presented through the conventional Delta parallel mechanism. The inverse kinematics was developed on the basis of the Pseudo-Rigid-Body (PRB) model. After the simplifying of the mass of passive arm and calculating the strain energy of the flexure hinges, the dynamic equation was established through the Lagrangian approach, and the natural frequencies are evaluated by utilizing the geometric parameters. Three natural frequency errors, which were along with three primary translation directions, between the experiment results and the theoretical analysis were 12.71%，12.14% and 14.90%. The error between the finite element simulation and the theoretical results were 6.20%，5.66% and 10.28%. The results also showed that the simplified process during the theoretical analysis was reasonable and the derived mathematics model was creditable.