Three-component all-fiber acceleration seismometer and its digital signal processing(DSP) system are developed. The seismometer is composed of a seismic mass, six cylinders and three sets of Michelson interferometer light path. The six cylinders are critical parts among the sensor elements. An advanced quality digital signal processing(DSP) chip equipped with necessary circuits has been used in its digital signal processing system, a high accurate detection of the acceleration signal has been achieved and the environmental interference signal has been effectively compensated. Test results indicate that the accelerometer has better frequency response above the resonant frequency, and the output signal is in correspondence with the input signal. The accelerometer also has better frequency response under the resonant frequency. At last, the curve of seismometer frequency response is given.