In order to improve the search ability of the cuckoo search algorithm, this paper proposes a quantum-inspired cuckoo search algorithm by introducing the quantum computing mechanism into the classical cuckoo search algorithm.. In the proposed algorithm, the qubits are used to encode individuals, and the Pauli matrixes are employed to determine rotation axis. The Levy flight principle is applied to obtain rotation angle, and the rotation of the qubits on the Bloch sphere is used to update the individuals. The experimental results of extreme optimization of benchmark test functions show that the proposed algorithm is obviously superior to the classical cuckoo search algorithm in optimization ability.