We present a twist compensated, high accuracy and dynamic fiber optic shape sensing based on phase demodulation in Optical Frequency Domain Reflectometry (OFDR) by using multiple single core fiber based sensor (MFS). A dynamic strain sensing is realized by tracking the optical phase in OFDR and combining with the phase de-hopping filtering algorithm, and the sensing spatial resolution reaches 45 μm. In addition, in order to eliminate the influence of external twist and fluctuation of inherent spin on the shape reconstruction results, we propose an external twist compensation method and inherent spin rate calibration method, respectively. Finally, we use a circle segment method to reconstruct a 3D shape of MFS. The experimental results show that the reconstruction accuracies by the proposed external twist compensation and inherent spin rate calibration methods increase over 18 times and 20 times than those without these two methods, respectively. At the same time, comparing with the traditional cross-correlation-based method, we find that the proposed phase demodulation method has a similar reconstruction accuracy, the maximum reconstruction error is 0.61 %, whereas the shape reconstruction speed is improved by nearly 10 times. This is of great significance for the application of FOSS, which can be used for dynamic shape sensing such as intelligent soft robots, surgical robot and etc.