In many industrial systems, the sensor is desirable to directly respond to a vector component associated with some physical phenomenon, such as the acceleration, velocity or displacement. This paper focuses on the application of fiber-optic accelerometers in oil well logging, presents a new design utilizing the combination of bellows structure and compliant material to enhance the unidirectional response of the fiber optic accelerometer. Furthermore, we accomplished a three components (3-C) acceleration sensing system by multiplexing three unidirectional sensing elements. Theory and experimental results show that our sensor can fulfill the demand of application in oil well logging, including responsivity, operation frequency range and directivity. The demodulated signal and the acceleration of vibration measured exhibit a linear relationship, and the suitable measurement frequency range of the system is between 3Hz and 800Hz. The on-axis sensitivity, cross-sensitivity and minimum detectable level is -101dB re V/ug, -135dB re V/ug and 39.3ug/Hz1/2, respectively.