Manifestly lorentz-invariant baryon chiral perturbation theory is used to calculate the radiative correction of low energy elastic lepton proton scatterings. Corrections of differential cross section and charge asymmetry are given at next-to-leading order with nonzero lepton mass, in which both are infrared and ultraviolet finite. The results are basically consistent with previous predictions based on hadron model, but somewhat different from calculations based on heavy baryon chiral perturbation theory, especially in charge asymmetry.