In this paper, some properties of a surface exciton in polyatomic polar crystals are studied. Effective Hamiltonians in the ground state of the surface exciton for both strong-coupling and weak-coupling-polyatomic polar crystals are obtained by the method of a linear combination operator and simple unitary transformation. The effective mass of a strong-coupling surface exciton is derived using a Lagrange multiplier method. The self-trapping energy and effective potential of the surface exciton could be written as a series in alpha _s^-1, the first term being proportional to alpha _s, the coupling constant. The self-trapping energy and effective potential contain an extra contribution due to crossed terms between the different phonon branches. For a surface Wannier exciton the increasing part of the effective mass is proportional to alpha _s.