Many exoskeleton systems use a cable-pulley mechanism for actuation for complex hand grips. This paper discusses a trajectory control of a finger using a mathematical model. The soft glove is designed based on the conceptual framework of a natural skeletal finger. A two-link mechanism forms the kinematic model of the finger joints and soft actuators. The design has a natural claw-like position for distal and middle phalanges during flexion. The cable passes through specially designed pulleys and anchors. An experiment is conducted to validate the controller model in predicting the finger position. A flex sensor measures the actual joint angle during flexion. The results indicate that the model is accurate in attaining the desired angular displacement. The controller is more accurate for lower joint angles of the finger. The model demonstrates potential in Continuous Passive Movement (CPM), task training exercises, and rehabilitation applications.