Force control technology plays a pivotal role in manipulating vulnerable objects. This paper presents a new compliant mechanism with constant-force output characteristics, which can prevent force damage due to displacement overshoot. Due to its unique passive structure, it is exempted from intricate sensors and complicated controllers. The quasi-static constant-force mechanism is obtained by the parallel combination of positive- and negative-stiffness mechanisms. Such a straightforward method facilitates a rapid development and implementation process. The procedures of architectural arrangement selection, theoretical model establishment, parameter sensitivity evaluation, and multi-objective structural optimization are carried out to achieve specified constant-force characteristics. Moreover, the prototype fabrication and performance testing of a constant-force mechanism have been performed. The results demonstrate that the mechanism delivers a constant output force of 339 mN in the motion range of 1.84 mm. The constant-force feature is solely governed by the actuating displacement and is independent of driving speed and acceleration. The promising application of the constant-force mechanism has been demonstrated by manipulating small force-sensitive objects such as biological eggs.