As a non-invasive imaging method, electrical impedance tomography (EIT) technology has become a research focus for grounding grid corrosion diagnosis. However, the existing algorithms have not produced ideal image reconstruction results. This article proposes an electrical impedance imaging method based on sparse representation, which can improve the accuracy of reconstructed images obviously. First, the basic principles of EIT are outlined, and the limitations of existing reconstruction methods are analyzed. Then, an EIT reconstruction algorithm based on sparse representation is proposed to address these limitations. It constructs constraints using the sparsity of conductivity distribution under a certain sparse basis and utilizes the accelerated Fast Iterative Shrinkage Threshold Algorithm (FISTA) for iterative solutions, aiming to improve the imaging quality and reconstruction accuracy. Finally, the grounding grid model is established by COMSOL simulation software to obtain voltage data, and the reconstruction effects of the Tikhonov regularization algorithm, the total variation regularization algorithm (TV), the one-step Newton algorithm (NOSER), and the sparse reconstruction algorithm proposed in this article are compared in MATLAB. The voltage relative error is introduced to evaluate the reconstructed image. The results show that the reconstruction algorithm based on sparse representation is superior to other methods in terms of reconstruction error and image quality. The relative error of the grounding grid reconstructed image is reduced by an average of 12.54%.