Summary: The method of the convective heat transfer coefficient identification in a three-phase inverse design Stefan problem is presented in this paper. The convective heat transfer coefficient will be sought in the form of a continuous function, non-linearly dependent on the parameters sought. A genetic algorithm was used to determine these parameters. The direct Stefan problem was solved via a generalized alternating phase truncation method. Stability of the whole algorithm was ensured by applying the Tikhonov regularization technique.