This paper presents the mechanical design of a novel 3-PSS (P and S represent the prismatic and spherical joints, respectively) parallel-kinematic flexure nanopositioning stage. This stage provides a high-precision motion driven by three piezoelectric actuators. By employing the compound displacement amplifier and 3-PSS parallel mechanism, the flexure nanopositioning stage can deliver two rotational degree-of-freedom (DOF) and one translational DOF. Statics modeling and dynamics analysis of the nanopositioning stage are carried out to evaluate the performance of the stage. To verify the accuracy of the analytical modeling, simulation studies with finite element analysis (FEA) are carried out. Results demonstrate the promising performance of the designed spatial nanopositioning stage for dexterous micromanipulation applications.