The squeezing properties of a two-mode field initially in a coherent state resonantly interacting with a three-level V-type atom are investigated by means of the quantum theory and numerical calculations. The dependence of the squeezing on the average photon number of the cavity mode,the coupling constant and the interaction time is discussed for three cases:1) no state-selective atomic measurement;2) direct state-selective atomic measurement;3) state-selective atomic measurement after the application of a classical field. It is show that the squeezing increases with the average photon number of the two cavity mode,and it is greatly enhanced if the atom is state-selectively measured even for the case of low photon number. It is concluded that the maximal squeezing is approximately 75% for all the considered cases.