A novel fiber Bragg grating (FBG) accelerometer based on an elastic structure which consists of a stainless steel tube and a mass block is proposed. Four FBGs are fixed axially on the tube surface where produce the most large strain along the circumference of the tube with a 90° angle. Two-dimensional measurement and temperature compensation are realized through the change of two pairs of FBGs′ wavelength shift caused by vibration. Finite element analysis is used to explain the two-dimensional measurement principle and the resonant frequency of the accelerometer further. Vibration test results demonstrate that the accelerometer possess of a resonant frequency of 515 Hz, a wide linear measurement range from 15 m/s2 to 75 m/s2 and a sensitivity of 0.88 pm·m-1·s2, which is consistent with the finite element analysis results. The two-dimensional vibration test results show that the accelerometer has a good anti-interference ability.