With the Mφller's theory of scattering between the electrons and the Dirac's hole theory, Bhabha has obtained the formula for the scattering of the electrons and the positrons. The experimental evidence of this phenomenon was discovered by Ho (何泽慧), and she has studied this phenomenon by means of the β+-radioactivity of the β+ sources such as Mn52, and F18 in the cloud chamber. The comparison of the theory and the experiment was done (see reference [2], [3], [4], [5] and [6].) by Ho, O. Ritter et al, R. R. Roy and L. Groven, G. R. Hoke and A. Ashkin et al.The purpose of the present work is to show the effect of the radiative corrections to the scattering of the electrons and the positrons by the method in the quantum electrodynamics developed by S. Tomonaga, J. Schwinger, R. P. Feynman and F. J. Dyson.In the above-mentioned electron and positron scattering experiments, the contributions to the scattering cross-section are mostly due to the positrons of low energies (about 0.1 to 0.2 Mev). In this energy range, the exchange effect in Bhabha's theory is small. In this work for the radiative corrections to the scattering of the electrons and the positrons, we have neglected this exchange effect. The ratio of the correction of the scattering cross-section due to the radiative corrections to the scattering cross-section of Bhabha's theory at this energy range does not exceed 1%. For experiments of the low energy positrons and of the higher energy positrons (e.g positrons with energies of 0.5 Mev to 1 Mev as in the experiment of Ashkin et al) with small exchanges of energy between the electrons and the positrons during scattering, our calculation is adequate. But for positrons of higher energies and with large exchanges during scattering, our calculation should be improved by considering the exchange effect.