  This paper presents an exact solution of Bardeen black hole in presence of
massive gravity, which is characterized by the additional parameter $m$. Here,
we focus on $4D$ Bardeen AdS massive black hole solutions as example to discuss
the thermodynamical properties such as temperature, entropy and specific heat
at constant pressure. We also study the critical behaviour of Bardeen AdS
massive black holes by considering the cosmological constant $\Lambda$ as
thermodynamical variable (pressure) as well as the parameter associated with
the nonlinear electrodynamics. We calculate the critical value of pressure and
temperature and study the effect of magnetic charge $e$ and mass parameter $m$.
It is seen that the thermodynamical volume are the independent of mass
parameter $m$. The critical values are the one in which phase transition takes
place and the nature of mass parameter $m$ and magnetic charge $e$ are opposite
to each other. The critical temperature and pressure were highly sensitive for
these parameters.
