A investigation of the properties of the bound states of D~- centers confined in a parabolic quantum dothas been performed for the case with the presence of a perpendicular magnetic field.Calculations are carried out byusing the method of numerical diagonalization of Hamiltonian matrix within the effective-mass approximation.Thebinding energies of the ground and some bound-excited states are obtained as a function of the applied magnetic fieldstrength.Detailed calculations of the binding energies for a number of low-lying states show that for field strength lessthan B=2.1 T,the D~- center confined in a quantum dot possesses two bound states,for 2.1≤B<2.4 T,there existthree bound states,etc.Further relevant characteristics of the D~- center quantum dots in magnetic fields are provided. A investigation of the properties of the bound states of D ~ - centers confined in a parabolic quantum dothas been performed for the case with the presence of a perpendicular magnetic field. Calculations are carried out by by the method of numerical diagonalization of Hamiltonian matrix within the effective -mass approximation. The binding energies of the ground and some bound-excited states are obtained as a function of the applied magnetic field strength. Betted calculations of the binding energies for a number of low-lying states show that for field strength lessthan B = 2.1 T , the D ~ - center confined in a quantum dot possesses two bound states, for 2.1 ≦ B <2.4 T, there exist bound free states, etc. Further relevant characteristics of the D ~ - center quantum dots in magnetic fields are provided.