The three-parameter two-mode squeezed number state is proposed by the technique of integration in an ordered product of operators. Its squeezing, antibunching effect and Cauchy-Schwartz inequality are analysed. The conditions under which squeezing or antibunching effect is displayed, are given. The effects of the complex parameter and photon number on squeezing , antibunching effect and Cauchy-Schwartz inequality of the field are discussed. The results indicate that its squeezing, antibunching effect and the degree of violation of Cauchy-Schwartz inequality of two-mode field are all weakened with the increase of photon number; on the other hand, its antibunching effect and the degree of violation of Cauchy-Schwartz inequality of two-mode field are weakened with the increase of the complex parameter modulus, while its squeezing is strengthened with the increase of the complex parameter modulus.