The nonclassical properties such as antibunching effect, violation of Cauchy-Schwarz inequality and two-mode squeezing of the pair coherent states based on a non-degenerate two-photon Jaynes-Cummings model were investigated. It is shown that these nonclassical properties can be enhanced in the case that the coefficients are chosen appropriately or the atom is selectively detected. In addition, all kinds of the nonclassical properties by using Ξ-type three-level atom are more effective than that using Λ-type three-level atom.