This paper proposes an electrical capacitance tomography algorithm based on an elastic network. To obtain feasible solutions, the L1 and L2 norms are used as the regular terms of the objective function, so that the solution has both the feature selection characteristics of the L1 norm and the image smoothing characteristics of the L2 norm. And utilize the normalized Laplacian as the weight of the elastic network, perform edge detection, and identify the dominance of L1 and L2. This algorithm makes the imaging region smooth, preserves the edge details of the image, and increases the accuracy of the image.