  Based on Reissner-Nordstrom-anti-de Sitter(RN-AdS) black hole surrounded by
perfect fluid dark matter, we study the thermodynamics and phase transition by
extending the phase space defined by the charge square $Q^{2}$ and the
conjugate quantity $\psi$, where $\psi$ is a function of horizon radius. The
first law of thermodynamics and the equation of state are derived in the form
$Q^{2}=Q^{2}(T,\psi)$. By investigating the critical behaviour of perfect fluid
dark matter around Reissner-Nordstrom-anti-de Sitter black hole, we find that
these thermodynamics system are similar to Van der Waals system, and can be
explained by mean field theory. We also explore the Ruppeiner thermodynamic
geometry feature and their connection with microscopic structure. We find that
in extended phase space there existence singularity points of Ruppeiner
curvature and it's could explained as phase transitions.
