A precision hi-directional actuator for a high precision leveling system with $Z{Theta}_x{Theta}_y$ motions is proposed and designed in this paper. The actuator is composed of a force generation structure, a guide mechanism, and a symmetric structure. At first, its driving force is generated by a change of flux in air gaps by permanent and changeable flux. The permanent flux is generated by a permanent magnet. The changeable flux is created by variable current flowing through coil. The combination of permanent and changeable flux makes various flux densities in air gaps between moving part and fixed yokes. And then, the difference between flux densities in lower and upper gaps creates forces fur the $bi-direction({pm}z)$ motion. The guide mechanism of this actuator is composed of two circular plates and one shaft. Reducing motions generated by forces except z-motion, these circular plates endow the actuator with high stiffness for fast settling time. And the function of the shaft is to transfer motion to an object. At last, total body has a symmetric structure to be stable on thermal error. The actuator is designed by MAXWELL 2D and ProMECHANICA. The designed actuator is evaluated by 8nm laser doppler vibrometer, dynamic signal analyzer, and simple PID controller.