Strain-controlled fatigue data of an austenitic stainless steel subjected to uniaxial state at different strain ratios with tensile and compressive mean strain are experimentally investigated to understand the fatigue phenomena when non-zero mean straining is involved. The fatigue test result indicates that mean stresses relax to very low level and the material experiences elastic-plastic response throughout the life. Moreover, the material has higher fatigue resistance under tensile mean strain loading condition than that of completely reversed loading and compressive mean strain cycling at the same strain amplitude which might be attributed to the micro-structural deformation mechanism. The capabilities of several damage parameters to characterize the non-zero mean strain effect on fatigue life are examined based on fatigue data and are found inappropriate for the as-received material. Therefore, a fatigue damage approach with a power law relationship between modified damage parameter and reversals to failure, considering a mean strain function in stress-strain-based fatigue damage module, is introduced to the material which shows better correlation with the uniaxial fatigue data under mean strain loading compared to that of some established fatigue models.