A magnetic quantum well created by putting two ferromagnetic metal stripes on the threedimensional topological insulator is investigated. The incident electron waves are confined in the quantum well by controlling the incident energy. The dispersion equation of the waveguide is obtained with the continuity of the wave functions. The graphical method is applied to solve this equation since it is a transcendental equation, of which the solution can not be obtained with analytic method. Whether the energy of the incident electrons is higher than the magnetic barrier or not, the electron waveguide can be formed. The waveguide supports the fundamental mode for the higher incident electron energy. The order of the modes increases with the increasing electron energy. The number of the guided modes decreases for the lower incident electron energy. The probability density of spatial distribution is studied. It shows that the threedimensional topological insulator waveguide induced by magnetic fields can confine electrons well and the lower guided modes can confine electrons better than the higher guided modes. Moreover, the function of the probability current density distribution in the waveguide is also presented.