  We study the possibility of an implementation of N-qubit (N>3) Grover search
in cavity QED, based on a fast operation of N-qubit controlled phase-flip with
atoms in resonance with the cavity mode. We demonstrate both analytically and
numerically that, our scheme could be achieved efficiently to find a marked
state with high fidelity and high success probability. As cavity decay is
involved in our quantum trajectory treatment, we could analytically understand
the implementation of a Grover search subject to dissipation, which would be
very helpful for relevant experiments.
