Precise control of the manipulating force within an appropriate range is crucial to prevent potential damage to the operating object. However, achieving accurate force control through force feedback is challenging in micro-scale applications. This study presents the design of a quasi-zero stiffness-compliant constant-force microgripper with adjustable force output. The parameters of the constant-force mechanism are designed using a model-based optimization method. By utilizing this mechanism, a compliant microgripper capable of providing adjustable constant-force output is developed to overcome the limitation of traditional grippers that offer only a single constant force. Finite element analysis is performed to simulate the behavior and verify the stability of the constant-force output. Furthermore, an experimental platform is constructed to validate the mechanical properties of the developed microgripper. The experimental results demonstrate that the automatically optimized structural parameters enable the microgripper to achieve the desired constant-force value of 2 N with an adjustable range of 0.15 N. These findings provide a further basis for the application and promotion of compliant constant-force structures.