A method and an apparatus for generating X-rays in which continuous X-rays can be generated by irradiating a focused laser in the air using a liquid as a target, thereby generating plasma. A high concentration electrolyte aqueous solution, such as CsCl and RbCl, is circulated by means of a pump (2) and the surface of a jet of high concentration electrolyte aqueous solution injected from a glass nozzle (3) is exposed to an irradiation of focused femtosecond laser pulse (6) via an objective lens (7), thereby generating X-ray pulses.