A novel type Brillouin optical time-domain analysis (BOTDA), called double-pulse BOTDA (DP-BOTDA), is proposed for measuring distributed strain and temperature in a fiber with a centimeter spatial resolution. The DP-BOTDA system transmits a double-pulsed light instead of a conventional single-pulsed light into a fiber to interact with a counter-propagating continuous-wave light through the induced acoustic wave in the fiber. The interference between acoustic waves induced by the front and rear pulses of the double-pulsed light produces broad but oscillatory Brillouin gain spectra that make it possible to measure the Brillouin frequency shift accurately despite the very narrow pulse width. Our numerical simulation, which includes an estimation of the signal-to-noise ratio of the system, shows that it is possible to measure the distributed Brillouin frequency shift with a spatial resolution of 4 cm and accuracies of 1-2 MHz for a 5-km long fiber.