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A kind of flexible pneumatic actuator (FPA) was introduced, and a new type of FPA-driven pneumatic flexible dexterous hand, named ZJUT Hand, was also proposed. Taking ZJUT Hand as the research object, the static model of the finger was established based on differential kinematics theory. Semi-closed loop control experiments for static force tracking of the finger were carried out. It was concluded from experimental results that fingertip output force could be controlled easily. Based on 5-component force/torque sensor installed on the fingertip, a control strategy for dynamic adaptive fuzzy fingertip force tracking was proposed. Experiments of dynamic fingertip force tracking were completed. Experimental results show that the control strategy can realize fast and accurate dynamic fingertip force tracking under an unknown environment. The response time is 1 s. The force tracking error is within ±0.15 N. 