Abstract: The fractal dimension and tribological characteristic of abrasive ?et finishing ( AJF ) surface investigated Experiments were performed on a cylindrical grinder MB1332A with a 45 # steel work piece as specimen with a surface roughness R_a of 0.6 μm The micromorphology and microcosmic geometry parameters of machined surface were measured with Micromesver2 profilometer .According to the metrical results , the surface topographies before and after finishing were evaluated with fractal dimension and power spectral density ( PSD ) .Effects of surface morphology and fractal dimension on the tribological characteristics of finished surface were also investigated with a MG -2000 pin –on-disk wear tester .The results showed that longitudinal geometry parameter values finished surface were reduced compared with that of the ground surface The mean ripple distance decreased ripple and peak densities increased The R_a gradually decreased from an initial value of about 0.6 μm to about 0. 2 μm with the increase of machining cycles The coefficient of friction and wear of finished surface were lower than that of ground surface The experimental results of tribological characteristics were in good agreement with the variation of fractal dimension