A method to deal with the electron impact excitation cross sections of an atom from low to high incident energies are presented. This method combines the partial wave method and the first Born approximation(FBA), i.e., replacing the several lowest partial wave cross sections of the total cross sections within FBA by the corresponding exact partial wave cross sections. A new set of codes are developed to calculate the FBA partial wave cross sections. Using this method,the convergent e–He collision cross sections of optical-forbidden and optical-allowed transitions at low to high incident energies are obtained. The calculation results demonstrate the validity and efficiency of the method.