  We investigate Einstein--Gauss--Bonnet--Maxwell massive gravity in $4D$ AdS
background and find an exact black hole solution. The horizon structure of the
black holes studied. Treating the cosmological constant as pressure and
Gauss-Bonnet coupling parameters, and massive gravity parameters as variables,
we drive the first law of black hole thermodynamics. To study the global
stability of the black holes we compute the Gibbs free energy. The local
stability of the black hole is also studied through specific heat. We analyze
the effects of graviton mass and Gauss-Bonnet coupling parameters on the phase
transition of the black holes. Finally, the effects of graviton mass and
massive gravity parameters on the Joule-Thomson expansion of the black hole are
studied.
