The traditional piezoelectric ceramic actuator has the inherent contradiction of high precision and large working stroke. To solve this problem, a novel 2R1T parallel precision positioning platform is proposed. It can be driven by the external force directly. The high precision and large working stroke can be both realized by the piezoelectric linear motor. Firstly, the influence mechanism of the structure parameters on actuation stroke is analyzed. Based on the analysis result, the flexible cylindrical flexible hinge with large working stroke is developed. Its structure parameters are optimized by using the fuzzy optimization method. Secondly, the 2R1T parallel precision positioning platform is established with three parallel branches, which are consisted of the two translation pairs and the flexible cylindrical flexible hinge. The kinematics model of the parallel platform is discussed by the coordinate homogeneous transformation method. The forward and inverse position solutions of the 2R1T platform are also obtained. Finally, experiments are implemented to evaluate the performance of the parallel platform. Experimental results show that the 2R1T parallel platform has advantages of synchronization and repeatability of positioning. By using the step motion mode of the piezoelectric motor, the parallel platform can realize the precise positioning. Its translation resolution is 009 μm, and the rotation resolutions are 08 μrad, 09 μrad and 10 μrad, respectively. In the continues motion mode of the piezoelectric motor, the large working stroke of the translation and rotation are 120 mm, 618°, 674° and 658°, respectively. The key performance indicators of precision positioning and large working stroke of the parallel platform are both realized based on different motion mode of only one piezoelectric motor. All basic research contents have important theoretical value and experiment foundation for the further study of the dynamical performance, the realization of precise positioning and control law of the 2R1T parallel platform.