Based on entanglement swapping, a scheme to generate the maximum entangled state by means of an entangled V-type three-level atomic system partially interacting with an entangled two-mode cavity field is proposed. In the scheme, the entanglement between the atom and the cavity field without any initial interaction can be achieved by measuring only a single atomic state without joint measurement. In the process of atom-cavity interaction, the cavity is only virtually excited and there is no energy exchange between the atom and the cavity, so the requirements of system on cavity quality are greatly relaxed. The results show that when the interaction time between the atom and the cavity field is 1.4675×10-5 s, the maximum entangled state with fidelity of 92.8% can be obtained. Moreover, the feasibility of the scheme is also discussed.