We have theoretically investigated the effect of structure parameters and applied external fields on the Ga1-xAlxAs/GaAs Konwent quantum well structure. Results of theoretical simulation have clarified the impact of applied external electric and magnetic fields, non-resonant intense laser field, as well as of the change in structure parameters, on the nonlinear optical rectification (NOR), second harmonic generation (SHG), and third harmonic generation (THG) in quantum wells with the Konwent potential. To evaluate these coefficients, we have solved the Schrodinger wave equation using the diagonalization method within the framework of the effective mass and single parabolic band approximations. Wave functions and the subband energy levels for the lowest bounded four states confined within the structure have been obtained. Then, NOR, SHG, and THG coefficient expression have been evaluated as functions of the incident photon energy. It is concluded that the appropriate choice of structure parameters and applied external fields could control the nonlinear optical properties of the Konwent potential quantum wells. The energy levels and the corresponding wavefunctions change with the applied external fields. The energy level change results in the shift of the peak position while the wavefunction change causes the variation in the dipole moment matrix elements, which affect the amplitude of the resonant peaks.