The squeezing properties of the two-mode atom laser in a system of Ξ-type three-level atomic Bose-Einstein condensate interacting with single-mode squeezed coherent light field are studied. The results show that the two-mode atom laser can be squeezed periodically, and has two types of oscillations: quantum Rabi oscillation and collapse-revival oscillation. The maximum depth of squeezing and the collapse-revival frequency of the atom laser depend greatly on the interaction intensity between the light field and atoms, and the quantum Rabi frequency is largely determined by the frequency of the light field.