Switched Reluctance Motor (SRM) is one of the best types of motors with a large number of merits; however, their torque profile faces with Torque Ripple (TR) especially in high speed which is known as an intrinsic drawback of these types of machines. The problem dramatically decreases the performance and popularity of SRMs. There are some strategies in order to reduce TR most of which are complex and expensive. In this paper, a novel low cost and simple method is presented in order to decrease TR. The method is based on using resonance phenomenon in the SRM conventional converter which is named asymmetric bridge converter or Two-Switch per Phase (TSP) converter. In the new Resonant Three-Switch per Phase (RTSP) converter, the energy stored in the phase winding discharges resonantly after switching off the phase which damps the phase current quickly. This dramatically reduces TR. After designing, the novel idea is simulated in MATLAB software and tested on a 6 by 4 three-phase SRM in laboratory. The SRM specifications are obtained by 3-D Finite Element Method (FEM) after simulation in MAGNET CAD software. Since then, the operational and simulation results of both TSP and RTSP converters are compared with each other. At the end of the paper, it has been shown that the RTSP converter not only significantly decreases the level of the generated TR but also improves the performance and efficiency of SRM.