Hand motions are important to humans in conducting daily life activities. Hand motion paralysis negatively affects the life quality of the involved patients. To recover the hand motions to their normal conditions, the patients must be involved in rehabilitation exercises in long-term treatments. These procedures require visual and interactive tools for supervising recovery progress. Previous studies tried to capture hand motions using contact sensors or devices, but they require complex facilities from the patients before use. A contactless solution will resolve these issues. Consequently, in this study, we develop a computer vision-based system for analyzing the hand motions. In the system, we employed a stereo camera to capture hand motion images in real time. The captured images will be fed into a Convolutional Neural Network (CNN) to detect all finger points. The detected finger points on the two stereo cameras were reconstructed into 3-D spaces using the stereo-vision geometries. The dimensions of finger motions were reduced into one dimension based on the principal component analysis (PCA). The cycles and plausible ranges of the motions were analyzed on the reduced spaces. As a result, we could successfully count the number of cycles and the plausible ranges of the finger motions. The method will be employed in our further clinical decision-support system for hand motion rehabilitation.