This paper presents the design and analysis of a new compliant constant-force gripper based on compound constant-force mechanism. The constant-force property can reduce the input force and prevent the object from damage without using a force feedback control. The compound constant-force mechanism contains an active and a passive constant-force structure. The active constant-force structure can reduce the input force, while the passive constant-force structure offers the safe interaction during the gripping operation. To evaluate the performance of the compound constant-force mechanism, analytical modeling is carried out, which is verified by conducting finite element analysis (FEA) simulation study. Results demonstrate the promising performance of the proposed mechanism design.