Super-Twisting Sliding-Mode Observer (STSMO) is a kind of second-order sliding-mode observer which has been widely used in position sensorless control of permanent magnet synchronous motor (PMSM), for it can significantly reduce the chattering phenomenon of system near sliding-mode manifold. In theory, a low-pass filter (LPF) is not necessary to STSMO because of its low-chattering character near sliding-mode manifold, and as a result, phase delay should not exist in the observing result of STSMO, which means that there is no need to compensate the rotor position estimated by STSMO with phase-locked loop (PLL). However, in practical situations, a number of non-ideal factors such as sampling delay and data-updating delay can affect the accuracy of STSMO estimation, especially in dynamic process. Error contained in electric angle estimated by STSMO can be very high without compensation, which will make the stability as well as performance of system worse. In this article, the idea that STSMO needs a close-loop angle compensation method while estimating rotor position is proposed. First, on the basis of the mathematical model of angle compensation method established in this paper, traditional angle compensation method based on PI regulator is analyzed, which reveals that PI method is approximately equivalent to using a sliding-mode controller with exponential reaching law to control the angle estimation error. To improve the dynamic compensation performance together with ability against disturbances, a variable-step close-loop angle compensation method using tangent reaching law is proposed from the perspective of sliding-mode control and reaching law. Then, to measure the dynamic performance and ability against disturbances of a compensation method, the definition of normalized compensation sensitivity is proposed. Calculation results of normalized compensation sensitivities of both algorithms show that tangent reaching law method has better ability against disturbances as well as dynamic performance. Finally, this conclusion is verified through simulations. The simulation results suggest that compared with traditional method based on PI regulator, this new algorithm does achieve better dynamic compensation performance and ability against disturbances while keeping a good steady-state compensation accuracy. Meanwhile, it also simplifies the design of compensation algorithm.