Abstract: Temperature field measurement of acoustic computer tomography calculates temperature distributions of the measurement region based on multi-path acoustic travel-times data.This paper studies the acoustic method to reconstruct the 3D temperature field.The sound wave propagation path model is established using the ray acoustics.Then a 3D temperature field reconstruction model is established based on radial basis function approximation with polynomial reproduction(RBF-PR) and a modified Tikhonov regularization method is presented,considering the sound wave propagation path in the non-uniform temperature field.The proposed method has reconstructed two kinds of temperature fields model under noise level of SNR=35 dB.3D display of reconstructed temperature fields and reconstruction errors are given with and without considering the bending of sound waves paths.And the 2D temperature field in a real boiler is reconstructed.The results indicate that the reconstruction accuracy can be improved obviously and the proposed method has strong anti-noise ability and good applicability.Therefore,it can be helpful for realizing high quality temperature reconstruction.