To meet the requirements for medium-high frequency vibration monitoring, a new type fiber Bragg grating (FBG) accelerometer with an integrative matrix structure is proposed. Two symmetrical flexible gemels are used as elastic elements, which drive respective inertial mass moving reversely when exciting vibration exists, leading to doubling the wavelength shift of the FBG. The mechanics model and a numerical method are presented in this paper, by which the influence of the structural parameters on the sensitivity and eigenfrequency is discussed. Sensitivity higher than 200 pm/g and an eigenfrequency larger than 3000 Hz can be realized separately, but both cannot be achieved simultaneously. Aiming for a broader measuring frequency range, a prototype accelerometer with an eigenfrequency near 3000 Hz is designed, and results from a shake table test are also demonstrated.