To solve the problems of complex structure and large computation of the traditional algorithm, a fast SVPWM algorithm based on three-section vector space is put forward. Without coordinate transformation, it uses the arithmetic in stead of complicated trigonometric operation, so it can reduce the number of logic judgment and get more accurate modulation. As a result, the algorithm structure of SVPWM is greatly simplified and the operation time is reduced. Besides, to improve the utilization ratio of DC bus voltage further, an over-modulation method based on piecewise nonlinear fitting is analyzed and raised, which can avoid the complex calculation of the holding angle and the control angle as well as the error of the modulation caused by look-up table method is also reduced. The results of simulation and experiment indicate that the fast SVPWM algorithm and its over-modulation method are effective and superior. This work is supported by Major Science and Technology Project of Guangdong Province (No. 2015B010118003) and Science and Technology Plan of Shandong Institutions of Higher Education (No. J17KB136).