Considering surface roughness and non-equal cross-section feature of tapered body and non-Newtonian characters of grease, fresh grease lubrication problem at two tapered bodies contact in the initial lubrication stage was analyzed, and effects of profile crowning, misalignment (tilting and skewing), sliding and loads were included. The multigrid method was applied to grease lubrication simulation by linear interpolation of rough surfaces and the discrete convolution and FFT (DC-FFT) was employed to compute elastic deformation. The results show that grease film thickness decreases with sliding aggravation. Both surface roughness and tilting motion will weaken the effectiveness of crowning and deteriorate the film bearing capacity. The adaptability of the tapered body with the cut-off profile to tilting motion is better than that with the logarithmic profile. However, if the cut-off profile is adopted, the crowning radius at small end of the tapered body should be larger than that at large end. The effect of minor skewing on grease lubrication is relatively slight. In a wide range of speed, the variation of traction coefficient is similar to the typical Stribeck curve, and the contact would experience three states of full-film, mixed and boundary lubrication.