Grinding is a popular method for producing high-quality parts made of hard and brittle materials. A lot of researchers have focused on the impact of grinding parameters on surface quality. However, only a few studies discussed the surface quality instability caused by the grinding wheel wear during a long grinding process. In this paper, through wheel state monitoring and surface quality testing of ground samples, it is found that the relationship between ground surface roughness and theoretical undeformed chip thickness is significantly affected by the grinding wheel wear state, rather than maintain steady as described in most available models. By introducing the normal grinding force, a linearly relationship was found among normal grinding force, undeformed chip thickness and ground surface roughness. Besides, sensitivity analysis was conducted to guide the parameter adjustment to maintain the stability of ground surface roughness and grinding state. The mechanism of the effect of wheel wear on normal grinding force was also studied in detail. This study will help to further understand the mechanism of the influence of wheel wear on the grinding stability.