In this paper,the interaction between surface electron and surface optical phonon for a strong coupling polyatomic polar crystals in magnetic field is studied.The ground state energies of a strong coupling and weak coupling surface magnetopolaron are obtained by the method of a linear combination operator and a simple unitary transformation.For weak coupling,we obtain the usual result that the groung state energy is the sum of the contribution of different phonon branches.For strong coupling,there is an extra contribution due to crossed terms between the different branches.