A general model of fiber Bragg grating (FBG) acceleration detector was established for the two-point package model. The sensitivity and the resonance frequency’s analytical expressions of the acceleration detector were deduced theoretically, the influence factors which affecting the sensitivity and resonance frequency were researched deeply, and the acceleration detector’s response characteristics were discussed, which would be affected by the ratio, that the package fiber stiffness to the structure stiffness. Based on this , the restrictive relation between theacceleration sensitivity and the resonance frequency with the increasing of the equivalent mass (0~100g ) was analyzed, respectively for the stiffness ratio in the range of 0~1 and 0~100. And the resonance frequency’s change rules within the scope of 0~500Hz (low-medium frequency) and 0~1200Hz (medium-high frequency) were also studied. Furthermore, the package fibers were chosen 10 mm and 60 mm as the examples to analyze the influence on the above two mentioned, the sensitivity of each simulation could reach up to ~1 000pm/G, and the quality factor was introduced. This study plays a significant role in the design and comprehensive performance evaluation of the acceleration detector, and can provide theoretical references for the optimization of structural parameters .