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Target-directed elbow movements are essential in daily life; however, how different task demands affect motor control is seldom reported. In this study, the relationship between task demands and the complexity of kinematics and electromyographic (EMG) signals on healthy young individuals was investigated. Tracking tasks with four levels of task demands were designed, and participants were instructed to track the target trajectories by extending or flexing their elbow joint. The actual trajectories and EMG signals from the biceps and triceps were recorded simultaneously. Multiscale fuzzy entropy was utilized to analyze the complexity of actual trajectories and EMG signals over multiple time scales. Results showed that the complexity of actual trajectories and EMG signals increased when task demands increased. As the time scale increased, there was a monotonic rise in the complexity of actual trajectories, while the complexity of EMG signals rose first, and then fell. Noise abatement may account for the decreasing entropy of EMG signals at larger time scales. This study confirmed the uniqueness of multiscale entropy, which may be useful in the analysis of electrophysiological signals.