Abstract <p>The eigenstates and density of states (DOS) of an anisotropic doped quantum dot (QD), as two essential quantities for understanding the band structure of the material, have been studied. We have solved the Hamiltonian, using the diagonalization method, in the presence of a perpendicular magnetic field, Gaussian impurity, and spin-orbit interaction (SOI): Rashba and Dresselhaus spin-orbit interaction terms. The spectra of the InAs-QD have been computed and plotted as a function of the Hamiltonian physical parameters. Furthermore, we have displayed the dependence of the DOS on the magnetic field strength, impurity position, and various Rashba and Dresselhaus spin-orbit interaction strengths. The results show that the impurity position (on and off) center significantly affects the spectra and the DOS. In addition, the presence of SOI partially removes the degeneracy of higher energy states and splits the Fock–Darwin states in the case of isotropic QD. The obtained results show that the issue of the anisotropy of the parabolic confinement has major effects on the DOS of the QD since it removes the degeneracy.</p>