In the present paper, we have studied the binding energy of the shallow donor hydrogenic impurity, which is confined in an inhomogeneous cylindrical quantum dot (CQD) of $\rm{GaAs-Al_{x}Ga_{1−x}As}$. Perturbation method is used to calculate the binding energy within the framework of effective mass approximation and taking into account the effect of dielectric mismatch between the dot and the barrier material. The ground-state binding energy of the donor is computed as a function of dot size for finite confinement. The result shows that the ground-state binding energy decreases with the increase in dot size. The result is compared with infinite dielectric mismatch as a limiting case. The binding energy of the hydrogenic impurity is maximum for an on-axis donor impurity.