  The phase structure of holographic entanglement entropy is studied in massive
gravity for the quantum systems with finite and infinite volumes, which in the
bulk is dual to calculate the minimal surface area for a black hole and black
brane respectively. In the entanglement entropy$-$temperature plane, we find
for both the black hole and black brane there is a Van der Waals-like phase
transition as the case in thermal entropy$-$temperature plane. That is, there
is a first order phase transition for the small charge and a second order phase
transition at the critical charge. For the first order phase transition, the
equal area law is checked and for the second order phase transition, the
critical exponent of the heat capacity is obtained. All the results show that
the phase structure of holographic entanglement entropy is the same as that of
thermal entropy regardless of the volume of the spacetime on the boundary.
