The structural safety and health inspection of carbon fiber reinforced polymer is very important. Electrical impedance tomography utilizes the conductive properties of carbon fiber composites to detect structural damage. This technology has the advantages of low cost, non-invasive and simple operation, and has become a research hotspot of scholars in recent years. There are serious ill-conditioned problems in the image reconstruction process of EIT. In this paper, an electrical impedance tomography algorithm with improved L1/2 regularization operator is proposed. The method uses the L1/2 norm to construct a sparse regularization penalty function, and uses the Bregman alternating direction method of multiplier iterative algorithm to solve the new objective function to improve the performance of the algorithm. To verify the effectiveness of the algorithm, four typical damage types of CFRP laminates were designed using COMSOL software and a 16-electrode EIT test system was built for verification. The simulation and actual experimental results show that, compared with other algorithms, using the BADMM iterative algorithm to solve the L1/2 regularization method improves the image correlation coefficient, reduces the image error, and effectively improves the accuracy of the reconstructed image, and the method has strong robustness to noise.