Using the single electron model, the acceleration of electrons in combined circularly polarized intense laser fields and the spontaneous quasistatic fields (including axial and azimuthal magnetic fields, the axial and transverse electric fields) produced in intense laser plasma interaction is investigated analytically and numerically by fitting the proper parameters of the quasistatic fields based on the data from the experiment and numerical calculation.A new resonant condition is given. It is found that the resonance acceleration of electron depends not only on laser field, but also on the bounce frequency oscillating in the quasistatic magnetic field and electric field. The net energy gained by electron does not increase monotonously with axial electric field, but there are some optimal axial electric fields.