We show theoretically that, based on the dispersive phase coupling effect during the wave mixing process, both slow and fast light can be achieved in GaAs–AlGaAs photorefractive multiple quantum wells (PRMQWs) films applied with a transverse direct-current electric field. The general formula for the group velocity of the diffracted beams in the Raman–Nath regime during the wave mixing process in a nonlinear thin film is derived and is then applied to the case of the PRMQWs films in the transverse geometry. The simulation results in the transverse-geometry PRMQWs films show that the group velocity and bandwidth of slow light can be on the order of centimeter per second and 100 kHz, respectively. The extremely low group velocity and the relatively broad bandwidth are mainly originated from the strong quadratic electro-optic effect and the fast response rate of the PRMQWs films, respectively. Our results show that the delay-bandwidth product of slow light can be significantly improved in PRMQWs films as compared to the reported results in other photorefractive materials.