Kinetic theory of sideband instability for an electromagnetic pump free-electron laser （EM-FEL） without a guided magnetic field has been developed by applying Vlasov-Maxwell equations and integration along the unperturbed orbit.The properties of electron motions in the equilibrium distribution have been discussed and the general dispersion equation is derived. The maximum linear growth rates and the relavent frequencies of sideband for step distribution have been obtained. Numerical calculations for the dispersion equations are carried out.The properties of the EM-FEL sideband instability have been discussed in detail.