Simultaneous effects of electric, magnetic, and non-resonant intense laser field on the nonlinear optical properties of a GaAs quantum well with an anharmonic confinement potential profile are theoretically investigated. Energy eigenvalues and eigenfunctions of the system are determined using the diagonalization method within the framework of the effective mass and parabolic band approximation. Nonlinear optical properties associated to the inter and intra band transitions are evaluated. Our numerical results for the intraband response show that the resonance peak positions of the total optical absorption coefficients and relative refractive index changes shift towards higher energy levels (blueshift) by increasing the strength of the applied external electric, magnetic, and non-resonant intense laser field. The analysis of inter-band (electron-heavy hole) transitions reveals that the optical coefficients has a pronounced redshift induced by the electric field while a blueshift is caused by the magnetic and laser signals. It is seen that the nonlinear optical properties of such structures can be adjusted according to the purpose by changing the external perturbations and could be used in new optoelectronic device designs.