This paper presents the design and testing of a novel flexure-based compliant parallel gripper with compound constant-force mechanism. One uniqueness of the microgripper lies in that it achieves two-degree-of-freedom (2-DOF) independent constant-force parallel grasping operations. In each direction, the grasping is executed along with active and passive constant-force properties. The passive constant-force property eliminates the use of force control while the active constant-force enlarges the grasping range by reducing the required driving force. Besides, the passive constant-force property can protect the grasped object from overloading. The parallel-kinematic flexure mechanism design enables nearly decoupled operations in 2-DOF manipulation. Analytical modeling of the microgripper mechanism is carried out based on pseudo-rigid-body method and elliptic integral approach, which is verified by conducting simulation study with nonlinear finite-element analysis (FEA). Parametric study is conducted to investigate the influence of dominant design variable on the microgripper performance. To demonstrate the performance of the gripper, a prototype is fabricated by 3D printer. Experimental results reveal that the devised microgripper owns a good decoupling performance and constant-force property in parallel grasping operation.