An effective-phonon-mode approximation (EPMA) for the polaron problem in a ternary mixed crystal A x B 1 - x C of semiconductors is suggested. The electron-phonon coupling constants, self-trapping energies and effective masses of a polaron in the system are calculated. It is found that the approximation is useful for III-V and II-VI compound mixed crystals, but a more complicated method is necessary for I-VII compounds. The effects of the unit-cell volume varying with the composition x of ternary mixed crystals are also investigated but proved unimportant.