The effects of nuclear isospin asymmetry on α-decay lifetimes of heavy nuclei are investigated within various phenomenological models of the nuclear potential for the α particle. We consider the widely used simple square-well potential and Woods-Saxon potential and modify them by including an isospin asymmetry term. We then suggest a model for the potential of the α particle motivated by a microscopic phenomenological approach of the Skyrme force model, which naturally introduces the isospin-dependent form of the nuclear potential for the α particle. The empirical α-decay lifetime formula of Viola and Seaborg [J. Inorg. Nucl. Chem. 28, 741 (1966)JINCAO0022-190210.1016/0022-1902(66)80412-8] is also modified to include isospin asymmetry effects. The obtained α-decay half-lives are in good agreement with the experimental data, and we find that including the nuclear isospin effects somehow improves the theoretical results for α-decay half-lives. The implications of these results are discussed, and the predictions on the α-decay lifetimes of superheavy elements are also presented.