A new kind of even and odd coherent states i.e.the photon-added and photon-deple ted states,can be obtained from acting boson inverse operators on the usual even and odd coherent states.The new states are the eigenstates of the operators a^ -ka^k+2 and a^+-ka2a^+k,r espectively.The results show that these states may reveal the anti-bunching and quantum squeezing effects.