In this paper, we investigate the P-V criticality and phase transition of charged accelerating AdS black holes in the extended thermodynamic phase space in analogy between black hole system and Van der Waals liquid-gas system, where the cosmological constant Λ is treated as a thermodynamical variable interpreted as dynamic pressure and its conjugate quantity is the thermodynamic volume of the black holes. When the electric charge vanishes, we find that no P-V criticality will appear but the

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... ing-Page like phase transition will be present, just as what Schwarzschild-AdS black holes behave like. For the charged case, the P-V criticality appears and the accelerating black holes will undergo a small black hole/large phase transition under the condition that the acceleration parameter A and the horizon radius r_h meet a certain simple relation A r_h=a, where a is a constant in our discussion. To make P-V criticality appear, there exists an upper bounds for constant a. When P-V criticality appears, we calculate the critical pressure P_c, critical temperature T_c and critical specific volume r_c, and we find that P_cr_c/T_c is an universal number.