Prediction of dynamic hand finger movements has many clinical and engineering applications in the control of human interface devices such as those used in virtual reality control, robot prosthesis and rehabilitation aids. Surface electromyography (sEMG) signals have often been used in the mentioned applications because these reflect the motor intention of users very well. In this study, we present a method to estimate the finger joint angles of a hand from sEMG signals that considers electromechanical delay (EMD), which is inherent when EMG signals are captured alongside motion data. We use the muscle activation obtained from the sEMG signals as input to a neural network. In this muscle activation model, the EMD is parameterized and automatically obtained through optimization. With this method, we can predict the finger joint angles with sEMG signals in both periodic and nonperiodic free movements of the flexion and extension movement of the fingers. Our results show correlation as high as 0.92 between the actual and predicted metacarpophalangeal (MCP) joint angles for periodic finger flexion movements, and as high as 0.85 for nonperiodic movements, which are more dynamic and natural.