Abstract: Acoustic wave propagation equations for two and three dimensional space were intensively investigated, and new algorithms for two and three dimensional acoustic path curve tracing based on the shooting method and the finite difference method were designed to track the acoustic path curves in the actual nonuniform temperature field. Acoustic path profiles were computed from numerical simulation and the enhancement effects of acoustic path tracking algorithms on the reconstruction of temperature fields with different gradients were verified. Results show that as the complexity of temperature field and the temperature gradient increase, the distribution of acoustic paths becomes more inhomogeneous, the acoustic paths deviate more from the straight line, and the reconstruction results based on acoustic refraction effect become more reliable. The proposed acoustic path tracing algorithms can quickly and accurately calculate the actual acoustic path curves and further improve the reconstruction accuracy based on acoustic tomography.