In order to realize new use of dexterous hand in the textile industry, a research method of twofingered dexterous hand of flexible fabric grasping was proposed. First, kinematics modeling of twofingered dexterous hand was established by using DH parameter method. Second, the trajectory planning of the twofingered dexterous hand was accomplished by quintic polynomial in the joint space. Finally, modeling and trajectory planning algorithm were verified and analyzed through simulation software. Simulation results prove that the model is accurate and reliable, and trajectory planning algorithm is reasonable, dexterous hand grasp mode is flexible, and it can grasp any shape flexible fabrics in the operating space. The research provides theoretical basis for entity dexterous hand system.