Because of its light weight, high power density, simple structure, continuous and soft movement, no noise in operation, no pollution to the environment and so on, the SMA(shape memory alloy) driver widely is used in dexterous hands. However, due to the requirement of the length of the drive wire, the driver can not be integrated into the palm of the hand. The SMA differential actuator with smaller structure size is designed to integrate the finger driver into the palm of the hand. The kinematic analysis of the single joint of the finger was carried out and the relationship between the driving current and the joint angle was obtained and the simulation analysis was carried out by using Matlab/Simulink. Finally, a driver experimental platform is built to verify the accuracy of the mathematical model of finger joints.