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The problem of bound polarons in quantum dot quantum well (QDQW) structures is studied theoretically. The eigenfrequencies of bulk longitudinal optical (LO) and surface optical (SO) modes are derived in the framework of the diclectric continuum approximation. The electron-phonon interaction Hamiltonian for QDQW structures is obtained and the exchange interaction between impurity and LO-phonons is discussed. The binding energy and the trapping energy of the bound polaron in CdS/HgS QDQW structures are calculated. The numcrical results reveal that there exist three branches of eigenfrequcncies of surface optical vibration in the CdS/HgS QDQW structure. It is also shown that the binding energy and the trapping energy increase as the inner radius of the QDQW structure decreases, with the outer radius fixed, and the trapping energy takes a major part of the binding energy when the inner radius is very small.