  Following the proposal by F. Yamaguchi et al.[Phys. Rev. A 66, 010302 (R)
(2002)], we present an alternative way to implement the two-qubit Grover search
algorithm in cavity QED. Compared with F. Yamaguchi et al.'s proposal, with a
strong resonant classical field added, our method is insensitive to both the
cavity decay and thermal field, and doesn't require that the cavity remain in
the vacuum state throughout the procedure. Moreover, the qubit definitions are
the same for both atoms, which makes the experiment easier. The strictly
numerical simulation shows that our proposal is good enough to demonstrate a
two-qubit Grover's search with high fidelity.
