The double-disc straight-groove (DDSG) grinding method is a new precision machining approach employed for the rolling surface of bearing rollers. The friction coefficient and wear resistance of grinding disc materials affect the grinding performance due to the operation on the workpiece. However, relevant research on DDSG is rather limited currently. Therefore, we analyzed the friction principles of the DDSG method and conducted friction and wear experiments to facilitate appropriate material selection for grinding discs. The optimal friction conditions for grinding disc materials were determined to ensure steady rotation of cylindrical rollers. In addition, the friction coefficients, wear resistance, and clogging resistance of various materials such as PTFE, PMMA, cast iron, brass, and fixed abrasives were measured by friction and wear experiments under grinding conditions. The friction pairs of PMMA-AISI 52100 and PTFE-AISI 52100 exhibited sliding friction coefficients of 0.14 and 0.03, respectively, along with a high grinding efficiency and excellent wear resistance. The friction pairs of both bearing steel-fixed abrasive and bearing steel-brass were easily clogged, leading to dramatic changes in the sliding friction coefficients, and neither fixed abrasive nor brass was found to be a suitable material for grinding discs. Thus, PMMA and PTFE were selected as the materials for upper and lower grinding discs. Moreover, a verification platform was built to implement the DDSG grinding method where a continuous rotation of ground roller was observed. Overall, this study provides a basis for feasible material selection and an appropriate material combination for designing a grinding machine based on DDSG.