The quantum statistical properties in the system of a two-mode SU(1,1)coherent field interacting with a two-level atom are investigated by solving Milburn equation. The effects on the quantum statistical properties induced by the intrinsic decoherence,the two-mode photon number and the mean photon number are analyzed. The results show that the intrinsic decoherence strengthens the anti-bunching effect of the two-mode and the correlation intensity between the two modes and makes the first mode of the field always to be sub-Poissonian. The second-order coherence degree of the two-mode field also exhibits obvious collapserevival effect with the intrinsic decoherence. The first mode of the field is sub-Poissonian with the evolution of the time. The photon anti-bunching appears and the correlation between the two modes of light is both positive and non-classical. But in most of the time,the second mode of the field is Poissonian with the evolution of the time and the photon bunching appears.