Fatigue damage on the train wheel surface was estimated by considering the effect of friction coefficient of rolling on the contact surface between the wheel and rail during operation. From FEM analys, the maximum Tresca stress was 550.7 MPa at a depth of 2.07 mm under the maximum contact pressure ($P_{max}$ = 894.3 MPa) between wheel and rail. The maximum stress continued to increase along with the increase in the frictional coefficient. The fatigue initiation lifetime of the wheel by the rolling contact was predicted using the Smith-Watson-Topper (SWT) equation and the maximum principal strain equation (${varepsilon}$-N).