The technique of Brillouin optical time domain analysis distributed optical fiber sensing has been presented and demonstrated experimentally, which is based on electrooptic modulation. Microwave electrooptic modulation is adopted to produce frequency-adjustable probe light, which is interacted with pulsed pump light via stimulated Brillouin scattering, when the optical frequency difference between probe and pump light is near the fiber's Brillouin frequency shift. The detecting signal of probe light is processed by digital BOXCAR and computer, then the fiber's Brillouin frequency shift could be obtained, and the distributing temperature or stress of the fiber could be calculated. The experimental procedures and results are presented. A laboratory system of 25 km distributed Brillouin optical time domain analysis temperature sensor is achieved, with 3 ℃ in temperature resolution, and 5 m in spatial resolution.