We investigated temporal behavior of an artificial two-level system driven by a strong oscillating field; namely, quantum-state evolution between two charge states in a small Josephson-junction circuit irradiated with microwaves. Rabi oscillations corresponding to 0-, 1-, and 2-photon resonances were observed. As a function of microwave amplitude, the Rabi frequencies followed a first-kind Bessel function of the corresponding order to the number of photons.