In order to assess the recovery of neural activity after stroke, it is necessary to select tasks that can be performed in the early stages of recovery. Since hand flexion is the first functional recovery that can be observed, it is a promising task to evaluate the recovery process. fMRI has reported that the amplitude of neural activity varies with the intensity of movement, but the correlation between movement and neural activity itself has not been reported in functional near-infrared spectroscopy (fNIRS). To investigate this, the present study performed simultaneous fMRI and fNIRS measurements in a healthy subject at different task intensities. The motor tasks were right and left hand grip movements. The motor intensity was set to 20% and 40% of maximum grip force. The grip pressure was recorded during the measurement. The results showed that the pressure was significantly higher in the 40% task than in the 20% task, and this occurred in both the left and right hand. In the motor cortex, fMRI showed that the percentage change in BOLD signal was greater in the 40% task than in the 20% task. fNIRS showed that deoxyhemoglobin concentration was significantly lower in the 40% task than in the 20% task, 9 seconds after the start of the task. Similar to fMRI, task-evoked hemodynamic responses were greater with greater motor intensity in fNIRS. Measuring hand grip movements with fNIRS could be a method to assess the neural recovery process in stroke motor paralysis.