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In order to overcome the shortcomings of traditional multi bar finger mechanism and meet more requirements of bionic finger at the same time, a design method of one degree of freedom non-circular gear five bar finger mechanism with position and pose points constraints of finger three joints was proposed. According to the actual size and motion position and pose of the finger, constraints of n position and pose points were established. The kinematic mapping theory and matrix singular value decomposition method were used to solve the hinge point curve meeting the requirements of the given constraints. According to the angular relationship between the two driving input rods, a non-circular gear pair meeting the requirements of position and pose points was designed, and the IO equation of one degree of freedom non-circular gear five bar finger mechanism was further deduced. On this basis, taking the five position and pose points constraint of three finger joint as an example, according to the other constraints of rod length, error, selection range of hinge points and non-circular gear transmission, the feasible curve solution domain was established. Finally, a one degree of freedom non-circular gear five bar finger mechanism parameters meeting all conditions was obtained, a finger mechanism prototype was developed and relevant tests were carried out. The experimental prototype showed that the design method proposed was correct and effective.