Carbon fiber reinforced polymer (CFRP) is electrically conductive, making it possible to detect structural damage of CFRP laminates with electrical impedance tomography (EIT). However, the inverse problem of EIT is severely non-linear, ill-posed, and underdetermined, thus limiting the resolution and accuracy of images reconstructed with EIT. This paper solves the inverse problem of EIT based on invertible neural networks (INN) and optimizes INN with Adamax gradient descent algorithm. Simulation and experimental results demonstrated that, compared with traditional EIT image reconstruction algorithms and radial basis function (RBF) neural network algorithm, the Adamax-INN model largely reduced the artifacts in reconstructed images, improved the damage recognition accuracy and edge clarity, and displayed good noise immunity.