In this paper, we propose a fault-tolerant control system for the position control and vibration suppression of a flexible arm robot. The proposed control system has a strain gauge sensor signal observer based on a reaction force observer and detects a fault by monitoring an estimated error. In order to improve the estimation accuracy, the plant parameters included in the sensor signal observer are updated by using the strain gauge sensor signal in normal time through the adaptive law. After fault detection, the proposed control system exchanges the faulty sensor signal for the estimated one and switches to a fault mode controller so as to maintain the stability and the control performance. We confirmed the effectiveness of the proposed control system through several experiments.