A theoretical investigation is carried out into the cross phase modulation (XPM) in an asymmetric double AlGaAs/GaAs quantum wells structure with a common continuum. It is found that, combining resonant tunneling-induced transparency and constructive interference in the third-order Kerr effect, a giant XPM can be achieved with vanishing linear and nonlinear absorptions, accompanied by the velocities of the probe and signal fields being matched. Furthermore, this giant XPM could induce a \pi-phase shift at a single-photon level which is favorable for the applications in two-qubit quantum logic gates.