The electron orbits in Gaussian beam′s laser wiggler are analysed.The single-particle orbits due to large amplitude,backward propagating pump laser field and axial guide magnetic field are derived,and the stabilities of the orbits are discussed.It is found that the results agree with that of the plane electromagnetic wiggler.Similiar to the orbits in magnetostatic wiggler in free-electron laser (FEL),the orbits in pump laser field have two classes of orbits.However,different from the orbits in a magnetostatic wiggler,the two classes of orbits in pump laser are stable.