Aiming at the influence of errors on three-dimensional fiber Bragg grating (FBG) accelerometers used in precision measurement and long-term monitoring, an error analysis and consistency assessment method based on Allan variance is proposed. An error model for the FBG accelerometer is established, and the Allan variance noise characteristics along three orthogonal axes are analyzed. The consistency of the three-axis performance is evaluated, and possible causes of inconsistency are investigated. By varying the correlation time τ of the sample subsets in the Allan variance analysis, the characteristics of different random processes at different time scales are further investigated. Based on experimental results, an error analysis of the three-dimensional FBG accelerometer is conducted, and the main error sources are identified, providing an important theoretical basis for performance optimization and error compensation of this type of geophone.