In order to solve the inherent contradiction of high precision and large working stroke in the traditional piezoelectric ceramic actuator, two motion modes of nonresonant piezoelectric actuator can be used to realize the high precision positioning and large working stroke. A new novel rhombic piezoelectric actuator is developed by designing the stator structure and the clamped pretensioning structure, and the working principle is also analyzed. The experimental results show that the positioning resolution is 1.0μm in the step motion mode, and the maximum motion speed is 0.932 mm/s in the continuous motion mode. On this basis, three rhombic piezoelectric actuators are synchronously applied to drive the parallel precision positioning platform. The translation resolution of the parallel platform is 1.0μm based on the step motion mode, and the rotation resolutions are 8.6, 11 and 10μrad, respectively. The excellent synchronization and repeatability of the parallel platform are also be proved by implementing the experiments for 10 times, and the fluctuation ratio of the repeatability data is less than 5%. In addition, the large working stroke of the translation and rotation are 3.54mm, 3.92°, 4.16° and 4.05°, respectively, in the continues motion mode of the piezoelectric motor. The key performance indicators of precision positioning and large working stroke of the parallel platform are both realized based on the different motion modes of only one piezoelectric motor. All of the above methods have a theoretical and experiment foundation for the further study of the dynamical performance and control law of the precision parallel platform.