In recent years, many sensors made of hard materials have been designed to detect human body movements in physical exercises. However, hard materials usually cause extra dyskinesia for body movements. To detect human limb motion with less dyskinesia in physical exercise, a novel flexible capacitive angle sensor (NFCAS) based on a conductive textile was designed in this paper. The NFCAS has two non-parallel plates, namely, an exciting plate and a sensing plate, which can be fixed onto the inner forearm and the inner upper arm. Thus, the angle between the two plates of the NFCAS can be used to represent the angle of medial elbow, and its variation can lead to changes in the sensor's capacitance at the same time. A push-ups experiment and pull-ups experiment were conducted to evaluate the designed NFCAS's performance. Experimental results showed that the NFCAS could detect the main processes of push-ups and pull-ups. Besides high measurement precision, the NFCAS is also soft, thin, lightweight, and easily made. Therefore, it can be widely applied for detecting human limb motion with less dyskinesia in physical exercises.