Micro-electromechanical system (MEMS)-based sensors play a vital role in the future of smart sensing applications owing to their small size, low power consumption, and cost-effectiveness. The issue of cross-axis sensitivity is of utmost importance when designing two-dimensional acceleration sensors. In this paper, we present the design of a two-dimensional acceleration sensor and investigate how the vibrations in different directions affect its sensitivity. A theoretical model, in which the effects of fabrication errors and air damping are considered, is built to investigate the sensor’s operation characteristics and optimize the sizes of the sensor’s spring systems in order to reduce cross-axis sensitivity. The results show that the cross-axis sensitivities in two-dimensional acceleration sensors have very small values, namely, 0.014% in the X-direction and 0.00649% in the Y-direction. The findings of this study are useful for the computation and development of two-dimensional acceleration sensors for high-precision measurements.