  In this paper, we investigate the thermodynamics especially the
Hawking-Page-like phase transition of the McVittie space-time. We formulate the
first law of thermodynamics for the McVittie black hole, and find that the work
density $W$ of the perfect fluid plays the role of the thermodynamic pressure,
i.e. $P$:=$-W$. We also construct the thermodynamic equation of state for the
McVittie black hole. Most importantly, by analysing the Gibbs free energy, we
find that the Hawking-Page-like phase transition from FRW spacetime to McVittie
black hole is possible in the case $P>0$.
