In this study, we have examined, under the influence of an electric field applied along the z-direction, the binding energy Stark-shift, the dipole moment and the polarizability of a confined shallow donor impurity in GaAs conical-shaped quantum dots (CSQD). With square infinite confinement system, the calculations are based on the approximation of the effective mass by using the finite difference method. Our results show that increasing the radius of the CSQD structure and the electric field intensity increases the Stark shift binding energy and it has a mixed behavior as a function of the impurity position. Furthermore, the polarizability and the dipole moment vary in a quasi-linear way as a function of the dot radius and they follow a decreasing function as a function of the electric field intensity. These two physical parameters have a double behavior, they decrease with the position of the impurity in the strong confinement regime and they increase in the top regions of the quantum dot. These results provide a lot of information about the behavior of the electronic wave function which give more interesting ideas for the fabrication of optoelectronic devices.