Cross-axis sensitivity of single-axis optomechanical accelerometers, mainly caused by the asymmetric structural design, is an essential issue primarily for high performance applications, which has not been systematically researched. This paper investigates the generating mechanism and detrimental effects of the cross-axis sensitivity of a high resoluion single-axis optomechanical accelerometer, which is composed of a grating-based cavity and an acceleration sensing chip consisting of four crab-shaped cantilevers and a proof mass. The modified design has been proposed and a prototype setup has been built based on the model of cross-axis sensitivity in optomechanical accelerometers. The characterization of the cross-axis sensitivity of a specific optomechanical accelerometer is quantitatively discussed for both mechanical and optical components by numerical simulation and theoretical analysis in this work. The analysis indicates that the cross-axis sensitivity decreases the contrast ratio of the interference signal and the acceleration sensitivity, as well as giving rise to an additional optical path difference, which would impact the accuracy of the accelerometer. The improved mechanical design is achieved by double side etching on a specific double-substrate-layer silicon-on-insulator (SOI) wafer to move the center of the proof mass to the support plane. The experimental results demonstrate that the modified design with highly symmetrical structure can suppress the cross-axis sensitivity significantly without compromising the sensitivity and resolution. The cross-axis sensitivity defined by the contrast ratio of the output signal drops to 2.19% /0.1g from 28.28%/0.1g under the premise that the acceleration sensitivity of this single-axis optomechanical accelerometer remains 1162.45V/g and the resolution remains 1.325μg.