The extended thermodynamics of static charged AdS black holes in conformal gravity is analyzed. The P–V criticality of these black holes has some unusual features. There exists a single critical point with critical temperature Tc and critical pressure Pc. At fixed T>Tc (or at fixed P>Pc), there are two zeroth order phase transition points but no first order phase transition points. The systems favors large pressure states at constant T, or high temperature states at constant P.