In the present work, the exact diagonalization method had been implemented to calculate the ground state energy of shallow donor impurity located at finite distance along the growth axis in GaAs/AlGaAs heterostructure in the presence of a magnetic field taken to be along z direction. The impurity binding energy of the ground state had been calculated as a function of confining frequency and magnetic field strength. We found that the ground state donor binding energy (BE) calculated at c ω =2R * and * 0 ω = 5. 421R, decreases from BE=7. 59822 R * to BE=2. 85165 R *, as we change the impurity position from d=0. 0 a* to d=0. 5 a*, respectively. In addition, the combined effects of pressure and temperature on the binding energy, as a function of magnetic field strength and impurity position, had been shown using the effective-mass approximation. The numerical results show that the donor impurity binding energy enhances with increasing the pressure while it decreases as the temperature decreases.