Nonclassical properties of a two-mode field initially in a SU(1,1) coherent state resonantly interacting with a Ξ-type three-level atom are investigated numerically. The influences of the initial intensity of the light field, the coupling constant and the selective atomic measurement on the sum squeezing of the light field, the sub-Poisson distribution of photon, the mode-correlation properties and the Cauchy-Schwarz inequality are discussed. The results indicate when the initial intensity of the light field is increased or the direct state-selective measurement is performed on the atom, the sum squeezing of mode b is distinctly enhanced, and mode b always exhibits the sum squeezing. When the initial intensity of the light field is small and the direct state-selective measurement is performed on the atom, the two modes always exhibit the sub-Poisson distribution. The correlation of the two-mode light is both positive and non classical, and the Cauchy-Schwarz inequality is violated.