A brief introduction to evaluating the beam size with the Root-Mean-Square (RMS) value, the full-width-half-maximum (FWHM) value and the modulation-transfer-function (MTF) value is given in this paper. The focusing of the long pulse electron beam (～100 ns) in an induction linear accelerator is studied by both theoretical analysis and numerical simulation, the contribution of the energy and current difference of the rising edge and the falling edge to the final beam size are discussed. In our results, the rising edge and the falling edge of the beam with large energy deviation may lead to a significant increase of the beam size, especially the MTF beam size, i.e. the FWHM beam size is increased by about 9% while the MTF beam size is increased by about 24%.