A distributed pressure sensor is proposed and designed for dynamic pressure measurement by using frequency-agile fast Brillouin optical time-domain analysis (BOTDA). A double coated single-mode fiber (SMF) is used as the sensing fiber because of its 1500- $\mu \text{m}$ thickness outer coating that can significantly improve the dependence of the Brillouin frequency shift on pressure. Then, the frequency-agile technique is used to generate frequency-agile pump pulse in BOTDA system so that a fast Brillouin gain spectrum distribution measurement can be achieved. An injection locked scheme is used as both optical filter and optical amplifier to improve the measurement accuracy. As a result, the static pressure sensitivity of the double coated fiber is −3.46 MHz/MPa with the pressure ranging from 0 to 30 MPa. Subsequently, a large dynamic range pressure measurement is performed with a sampling rate of 33.3 kHz and maximum sensing distance of 25 m. Furthermore, it is proved that the uncertainty of dynamic pressure measurement system is 0.03 MPa.