  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 chiral next-to-leading order $(\mathcal{O}(p^2))$ with a nonzero
lepton mass, which are infrared and ultraviolet finite. The results are
basically consistent with previous predictions based on hadron model
calculation, but they are somewhat different from calculations based on heavy
baryon chiral perturbation theory, especially in charge asymmetry.
