A linear piezoelectric stack actuator used for the focus adjustment system of an interference microscope was proposed and a micropositioner was also developed. The structure of the actuator was designed based on the principle of triangle displacement amplification. The modeling of the steel frame structure was realized by parameter design language APDL in the ANSYS, and the parameters of the structure were optimized by the optimization algorithm of Differential Evolution (DE) in Optimus. A experimental prototype for the actuator was produced, and laser interferometric experiment shows that the actuator's amplification factor reaches 7 when the drive voltage is between 40 V and 100 V. Finally, the piezoelectric stack actuator was mounted on the micropositioner to be a driver for an interferometer. Experiments show that the step resolution of the micropositioner with flexure hinges has reached 23 nm under the system voltage of 24~40 V and an increment voltage of 0.8 V. These data meet the requirement of interferometric fringe of interference microscope for linear displacement resolution.