We report on the energy exchange between femtosecond laser filaments in air. A traveling plasma grating formed at the intersection of the filaments is proposed to explain the energy transfer. In this moving plasma grating mediated mechanism the laser energy transfers from the lower frequency pulse to its higher frequency partner, while in a traditional Kerr nonlinearity mediated grating, energy transfer occurs in the opposite manner. Based on this mechanism, we demonstrate an energy transfer ratio as high as 50% for pulses with an energy of several millijoules.