We study two flux qubits with a parameter coupling scenario. Under the rotating wave approximation, we truncate the 4-dimensional Hilbert space of a coupling flux qubits system to a 2-dimensional subspace spanned by two dressed states ｜01} and ｜10}. In this subspace, we illustrate how to generate an Aharnov Anandan phase, based on which, we can construct a NOT gate （as effective as a C-NOT gate） in this coupling flux qubits system. FinMly, the fidelity of the NOT gate is also calculated in the presence of the simulated classical noise.
