An important question in motor neuroscience is how the nervous system controls the spatiotemporal activation patterns of redundant muscles in generating accurate movements. The redundant muscles may not only underlie the flexibility of our movements but also pose the challenging problem of how to select a specific sequence of muscle activation from the huge number of possible activations. Here, we propose that noise in the motor command which has an influence on task achievement should be considered in determining the optimal motor commands over redundant muscles. We propose an optimal control model for step-tracking wrist movements with redundant muscles that minimizes the end-point variance under signal-dependent noise. Step-tracking wrist movements of human and non-human primates provide a detailed dataset to investigate the control mechanisms in movements with redundant muscles. The experimental EMG data can be summarized by the two eminent features; 1) amplitude-graded EMG pattern, where the timing of the activity of the agonist and antagonist bursts show little variations with changes in movement directions, and only amplitude of activity is modulated, and 2) cosine tuning for movement directions exhibited by the agonist and antagonist bursts, and the discrepancy found between muscle's agonist preferred direction, and its pulling direction. In addition, it is also an important observation that subjects often overshoot the target. We demonstrate that the proposed model captures not only the spatiotemporal activation patterns of wrist muscles but also trajectory overshooting. This suggests that when recruiting redundant muscles, the nervous system may optimize the motor commands across the muscles so as to reduce the negative effects of motor noise.