A distributed feedback (DFB) fiber laser accelerometer sensor with a vertically encapsulated structure is designed. The theoretical models of the acceleration sensitivity and the dimension parameters of the mass block are established. Based on the finite element software, the frequency response performance of this accelerometer sensor is simulated. The prototype sample of the sensor is fabricated and tested. The experimental results show that the average acceleration sensitivity of the fabricated DFB fiber laser accelerometer sensor reaches -119.1 dB in the spectral range of 10 to 4000 Hz, and the resonant peak appears near the frequency of 5000 Hz, which agrees well with the theoretical and simulated results. The working frequency band of the fiber laser accelerometer sensor is effectively broadened towards high frequency, which can better meet the requirements of engineering applications of DFB fiber laser accelerometer sensors in the high frequency field.