In this paper, the design of a new compliant XYZ totally decoupled parallel-kinematic nanopositioning stage based on flexure mechanism is presented, which is driven by PZT actuators. The output of the flexure stage is enlarged by a compound amplifier of three order based on bridge principle with the amplification ratio of A_s^3 which is larger than the ratio of A_s for one simple amplifier. The three-dimensional amplifier can overcome the shortage of the displacement limitation of the actuator. The flexure stage with three actuators can obtain the motion along X, Y and Z axes with cross-axis errors less than 1% and the natural frequency larger than 100 Hz. In order to verify the dimension of the objective stage simulation GA method is conducted. FEA simulation results demonstrate the performance of the designed multi-axis nanopositioning stage.