A fiber grating accelerometer with adjustable sensitivity belongs to the machinery vibration testing technology field, and comprises a housing, and a fiber grating, a L-type rotary shaft, a support, a mass block, an isostrenth beam, a motion steel shaft, and a steel sheet arranged in the housing; the rotary shaft is supported on the housing bottom plate by the support, and penetrates the steel sheet; one end of the rotary shaft is connected on the housing end plate, and the other end is connected with the mass block; the mass block freely slides along the rotary shaft; the isostrenth beam with the bonded fiber grating is fixed on the housing end plate, has the same height with the rotary shaft center, and the end of the isostrenth beam is connected with a motion steel shaft; the motion steel shaft is connected with the edge of the steel sheet on the rotary shaft. The mass block is provided with a plurality of shifts on the rotary shaft; according to measuring requirements of a measured object, the mass block can slide on the L-type rotary shaft so as to select the property shift, thus flexibly adjusting the sensitivity and measuring range, and improving measuring precision in the selected measuring range.