A new method of generation of nanosecond soft X-ray pulses with a photon energy around 1 keV is presented. X-rays are generated in a high-temperature plasma, which is created as a result of the interaction of Nd:glass laser radiation with a gas puff target. The target was obtained by puffing a small amount of gas through the nozzle into the vacuum chamber by means of a pressure electromagnetic valve. The pulses of laser radiation, with pulse duration of 1 ns and energy up to 15 J, generated in the system of a high-power Nd:glass laser were used for the target heating. Spatial, spectral, and temporal measurements of X-ray emission have shown that the high-intensity soft X rays are generated as a result of the interaction of nanosecond pulses of Nd:glass laser radiation with the gas puff target. A high efficiency of X-ray generation is suggested to be related to the effect of condensation of the gas outflowing from the valve nozzle and, in effect, to the interaction of laser radiation with matter in a form of aerosol.