Voltage controlled magnetic anisotropy (VCMA) is a low-energy alternative to manipulate the ferromagnetic state, which has been recently considered also in antiferromagnets (AFMs). Here, we theoretically demonstrate that VCMA can be used to excite linear and parametric resonant modes in easy-axis AFMs with perpendicular anisotropy, thus opening the way for an efficient electrical control of the Néel vector, and for detection of high-frequency dynamics. Our work leads to two key results: (i) VCMA parametric pumping experiences the so-called "exchange enhancement" of the coupling efficiency and, thus, is 1-2 orders of magnitude more efficient than microwave magnetic fields or spin-orbit-torques, and (ii) it also allows for zero-field parametric resonance, which cannot be achieved by other parametric pumping mechanisms in AFMs with out-of-plane easy axis.Therefore, we demonstrate that the VCMA parametric pumping is the most promising method for coherent excitation and manipulation of AFM order in perpendicular easy-axis AFMs.