We propose a scheme for implementing Grover quantum search algorithm based on the qubit-qubit interaction in circuit QED. We show how to implement the proposed quantum search algorithm using two-transmon-qubit in a circuit QED driven by a strong microwave field. The implementation time is a time of nanosecond-scale, which is much smaller than decoherence time and dephasing time, both being the time of microsecond-scale. Numerical simulation under the influence of the Grover algorithm shows that our proposal is realizable with high fidelity. We propose a detailed procedure and experimentally analyze its feasibility. Moreover, the scheme might be experimentally achieved efficiently with presently available techniques.