We study the effect of the nonparabolicity of the conduction band on the spectral properties of the shallow donor in elongated InAs/GaAs quantum dots with volcano-shaped profile in the framework of the Kane model by using a simple semiempiric relation between geometrical parameters of the quantum dot profile and the confinement potential, governing the in-plane electron’s movement. We represent the solution of the Schrödinger equation in the form of double Bessel-Fourier series expansion. We show that the nonparabolicity of dispersion of the conduction band, given by the Kane formula, conduces to significant lowering of the donor energies and to stronger confinement of the electron within the quantum dot. Calculated results for the energies as functions of the electric and magnetic fields for different quantum dot dimensions were compared with those obtained in the effective mass approximation. Our results exhibit a high sensibility of the probability density of electron distribution in volcano-shaped quantum dot to the variation of the external magnetic and electric fields.