We present a novel method for measuring the frequency response of a diaphragm-based optical fiber Fabry-Perot interferometric pressure sensor. The impulse response of the sensor to the radiation pressure generated by an excimer laser pulse is measured. The Fourier transform of the impulse response yields the frequency response of the pressure sensor. Experimental results show that it is a convenient and efficient method for measurement of the frequency response of diaphragm-based pressure sensors.