  We study the P-V criticality and phase transition in the extended phase space
of charged anti-de Sitter black holes in canonical ensemble of ghost-free
massive gravity, where the cosmological constant is viewed as a dynamical
pressure of the black hole system. We give the generalized thermodynamic first
law and the Smarr relation with massive gravity correction. We find that not
only when the horizon topology is spherical but also in the Ricci flat or
hyperbolic case, there appear the P-V criticality and phase transition up to
the combination k+c02c2m2 in the four-dimensional case, where k characterizes
the horizon curvature and c2m2 is the coefficient of the second term of massive
potential associated with the graviton mass. The positivity of such combination
indicate the van der Waals-like phase transition. When the spacetime dimension
is larger then four, the Maxwell charge there seems unnecessary for the
appearance of critical behavior, but a infinite repulsion effect needed, which
can also be realized through negative valued c3m2 or c4m2, which is third or
fourth term of massive potential. When c3m2 is positive, a Hawking-Page-like
black hole to vacuum phase transition is shown in the five-dimensional
chargeless case. For the van der Waals-like phase transition in four and five
spacetime dimensions, we calculate the critical exponents near the critical
point and find they are the same as those in the van der Waals liquid-gas
system.
