We have studied the effects of the wake field on the energy spectrum of a high-intensity single-bunch electron beam of 28 nC charge accelerated in an L-band accelerating structure of 1.3 GHz frequency both by experiment and by calculation. Energy spectra measured as a function of the accelerating phase show significant changes, including appearance of multiple peaks owing to the short-range longitudinal wake field. The empirical wake function is derived for the specific accelerating structure using the simulation code, ABCI. Energy spectra calculated with the wake function agree quite well with the energy spectra measured over the wide range of the accelerating phase. The effects of the wake field on the energy spectrum of the high-intensity single-bunch beam accelerated with the L-band linac at Institute of Scientific and Industrial Research (ISIR), Osaka University, are quantitatively explained in terms of the wake field theory with the empirical wake function.