As a convenient and feasible measure of postural control, centre-of-pressure (CoP) trajectories are investigated in most of postural research. The characteristics extracted from CoP trajectories provide valuable evidences in nature explorations of postural control. In this research, Shannon entropy is introduced into CoP trajectories analysis to reveal random characteristics of human upright postural control. In our Shannon entropy analysis, chaos level of CoP single-step displacement is inspected in static and dynamic visual conditions. Experimental results from twenty-one subjects under four visual conditions indicate that human postural control in upright stance appears more regulated in direction control than in amplitude control. This conclusion has specific significance in postural experiment design and postural control improvement.