This study analyzed the precision grip force for the underactuated gripper for power and precision grasp (uGRIPP). uGRIPP is a robot hand developed for dual arm manipulation. It can grasp objects through power and precision grips. For a more detailed analysis of the performance on the grip force and control of the grip force, a relationship was derived between the grip and actuation forces by using an analytical method based on the principle of virtual power. Finally, theoretical values of the grip force were calculated according to the analysis, and the actual grip force was measured experimentally. The experimental results show the validity of the analysis.