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