  We study thermodynamics of a charged AdS black hole in the special $f(R)$
correction with the constant Ricci scalar curvature. Our results show that the
the $f(R)$ correction influences the Gibbs free energy and the phase transition
of system. The ratio $\rho_c$ occurred at the critical point increases
monotonically with the derivative term $f'(R_0)$. We also disclose that the
critical exponents are the same as those of the liquid-gas phase transition in
the Van der Waals model, which does not depend on the $f(R)$ correction
considered here.
