Magnetic detection electrical impedance tomography (MDEIT) is a novel imaging technique that aims to reconstruct the conductivity distribution with electrical current injection and the external magnetic flux density measurement by magnetic sensors. Aiming at improving the resolution and accuracy of MDEIT and providing an efficient imaging method for breast cancer diagnosis, a new algorithm based on stacked auto-encoder (SAE) neural network is proposed. Both numerical simulation and phantom experiments are done to verify its feasibility. In the numerical simulation, an amount of sample data with different conductivity distribution are calculated. Then a neural network model is established and trained by training these samples. Finally, the conductivity distribution of an imaging target with the anomaly location can be reconstructed by the network model. The reconstruction result of the SAE algorithm is compared with the reconstruction results of the traditional sensitivity matrix (SM) algorithm and the back propagation (BP) neural network algorithm. Under the noise of 30dB, the relative errors of BP algorithm, SM algorithm and SAE algorithm are 137.19%, 24.90% and 15.28% respectively. Result shows by the SAE algorithm, the location of anomalies is reconstructed more accurately, the conductivity value is more closely to the real one and the anti-noise performance is more robust. At last, a breast phantom experiment by self-made platforms is completed to verify the application feasibility of the new algorithm. The relative reconstruction error of conductivity by proposed SAE algorithm can be reduced to 14.56%. The results show that by SAE algorithm, MDEIT can be a promising approach in clinical diagnosis of breast cancer, and it also provide more potential application prospect for the extensive application of MDEIT. INDEX TERMS Breast cancer diagnosis, inverse problem, magnetic detection electrical impedance tomography, stacked auto-encoder.