This study applied a comprehensive electroencephalography (EEG) analysis for movement-related cortical potentials (MRCPs) and event-related desynchronization (ERD) in order to understand movement-related brain activity changes during movement preparation and execution stage of unilateral wrist extension. Thirty-four healthy subjects completed two event-related potential tests in the same sequence. Unilateral wrist extension was involved in both tests as the movement task. Instruction Response Movement (IRM) was a brisk movement response task with visual “go” signal, while Cued Instruction Response Movement (CIRM) added a visual cue contenting the direction information to create a prolonged motor preparation stage. Recorded EEG data were segmented and averaged to show time domain changes and then transformed into time-frequency mapping to show the time-frequency changes. All components were calculated and compared among C3, Cz, and C4 locations. The motor potential appeared bilaterally in both tests' movement execution stages, and Cz had the largest peak value among the investigated locations (p < 0.01). In CIRM, a contingent negative variation (CNV) component presented bilaterally during the movement preparation stage with the largest amplitude at Cz. ERD of the mu rhythm (mu ERD) presented bilateral sensorimotor cortices during movement execution stages in both tests and was the smallest at Cz among the investigated locations. In the movement preparation stage of CIRM, mu ERD presented mainly in the contralateral sensory motor cortex area (C3 and C4 for right and left wrist movements, respectively) and showed significant differences between different locations. EEG changes in the time and time-frequency domains showed different topographical features. Movement execution was controlled bilaterally, while movement preparation was controlled mainly by contralateral sensorimotor cortices. Mu ERD was found to have stronger contra-lateralization features in the movement preparation stage and might be a better indicator for detecting movement intentions. This information could be helpful and might provide comprehensive information for studying movement disorders (such as those in post-stroke hemiplegic patients) or for facilitating the development of neuro-rehabilitation engineering technology such as brain computer interface.