In this paper, we study properties of diffraction of a weak probe field interacting with a symmetric semiconductor quantum well that is coherently manipulated by a standing wave. Based on the theory of quantum coherent and of light diffraction, we can obtain distribution of the diffraction spectra of the probe field. We consider the influences of Kerr nonlinear effect on the diffraction pattern, and studies show the distribution of diffraction pattern can be controlled through choosing appropriate physical parameters of system. Kerr nonlinear effect can enhance the brightness of central pattern and improve the transmission efficiency of the incident beam. A controllable diffraction pattern has potential applications in some areas, such as design of quantum diffractive optical elements, grating imaging system, precision measurement and so on.