Abstract: In order to improve the quality of the inversion in the elastic wave CT, at the same time, taking into account the pathological characteristics of the coefficient matrix and low quality of the reconstruction image obtained by the BPT-SIRT algorithm, a method based on principal component weighting preprocessing and weighted BPT-SIRT algorithm is proposed. The initial iterative value obtained by the method of BPT is weighted, then, adding a weight to the principal component of the coefficient matrix, the element of ray matrix is weighted by the nonlinear exponential weighting function. The method is verified by numerical simulation and concrete filled steel tube specimens with defects. The results show that the method has better convergence speed and accuracy, and the recognition effect is better.