A scheme is proposed for realizing quantum entanglement, information transfer,CNOT gates, and SWAP gates with superconducting-quantum-interference-device(SQUID) qubits in cavity QED. In the scheme, the two logical states of a qubitare the two lowest levels of the SQUID. An intermediate level of the SQUIDis utilized to facilitate coherent control and manipulation of quantum states ofthe qubits. The method presented here does not involve a real excitation of theintermediate levels during the operations. Thus, decoherence due to energy relaxation ofintermediate levels is minimized. In addition, the present method does not require theadjustment of the SQUID level spacings, which simplifies the operation significantly.