We analyze the effect of the potential shape on the ground state energy of the off-axis neutral donor in GaAs/Ga 1−x Al x As cylindrical nanotube in the presence of the uniform magnetic field applied along the symmetry axis. To take into account the mixing of the low lying subbands we express the wave function as a product of combination of 1s and 2p x,y wave functions with an unknown envelope function that depends only on electron-ion separation. By using variational principle and the functional derivative procedure we derive a one-dimensional differential equation for the envelope function, which we solve numerically by using of the trigonometric sweep method. Results of calculation of the ground state binding energy dependencies on the distance from the donor position to the axis and on the strength of the external magnetic field for square-well, soft-edge-barrier and parabolic bottom potentials are presented. It is shown that the additional peaks in the curves of the density of impurity states appear due to the presence of the repulsive core is nanotube.