  We present the cosmological analysis of the Gauss-Bonnet quasi-dilaton
massive gravity theory. This offers a gravitational theory with a non-zero
graviton mass. We calculate the complete set of background equations of motion.
Also, we obtain the self-accelerating background solutions and we present the
constraints on parameters to indicate the correct sign of parameters. In
addition, we analyse tensor perturbations and calculate the mass of graviton
and find the dispersion relation of gravitational waves for two cases. Finally,
we investigate the propagation of gravitational perturbation in the FLRW
cosmology in the Gauss-Bonnet quasi-dilaton massive gravity.
