The influence of nuclear deformation on α -decay half-lives is taken into account in the deformed density-dependent cluster model. The microscopic potential between the spherical α particle and the deformed daughter nucleus is evaluated numerically from the double-folding model by the multipole expansion method. A realistic density-dependent nucleon-nucleon (NN ) interaction with finite-range exchange part, which produces the nuclear matter saturation curve and the energy dependence of the nucleon-nucleus optical potential model is used. The ordinary zero-range exchange NN force, which is commonly used in α decay, is also considered in the present work. We systematically investigate the influence of nuclear deformations on the α -particle preformation probability of the deformed medium and heavy nuclei from the ground state to ground-state α transitions within the framework of the Wentzel-Kramers-Brillouin method by considering the Bohr-Sommerfeld quantization condition. Taking the deformation of daughter nuclei into account changes the behavior of the preformation probability, S α , by an amount depending on the Q value, the order, values, and signs of deformation parameters. Calculations have been conducted for the spherical nuclei in order to present clearly the effect of the deformation on the preformation probability. The combined effect of both finite-range force and deformation can reduce the value of S α by about an order of magnitude.