Aiming at the low resolution and low accuracy problems of image reconstruction in magnetic detection electrical impedance tomography currently, in this paper a new magnetic detection electrical impedance tomography algorithm based on stacked auto-encoder (SAE) neural network is proposed. Simulation experiment is conducted using a square imaging object. Using training samples, a SAE neural network model is established, the weight matrices and bias units of the neurons are determined. Then, the conductivity distribution inside the imaging object is reconstructed with the network model. The reconstruction results for the SAE neural network, such as the center position of the anomaly, the anti-noise performance of the algorithm and so on, are compared with those for the back propagation neural network based on the Levenberg-Marquardt algorithm. The results show that the stacked auto-encoder neural network algorithm significantly improves the reconstruction accuracy and anti-noise performance of the magnetic detection electrical impedance tomography. Finally, the phantom experiments were used to verify the feasibility of the SAE algorithm. From the measured magnetic flux density, the proposed SAE neural network algorithm was used to reconstruct the conductivity and accurately locate the position of the anomaly. The stacked auto-encoder neural network algorithm has great significance for the widespread usage of magnetic detection electrical impedance imaging technology.