The electrical conductivity of the small goaf under the power tower is significantly different from that of the surrounding rock, which makes it difficult for the frequency domain electromagnetic conductivity imaging of the small goaf to converge and depends on the initial iteration value. In order to expand the convergence range and improve the ill posedness of the inverse problem of frequency domain electromagnetic imaging in small goafs, this paper applies the Homotopy Tikhonov algorithm (HT-GN) to perform conductivity imaging in shallow small goafs using frequency domain electromagnetic imaging. Analyze the reconstructed images of small goaf under different initial iteration values using the proposed HT-GN algorithm; The results show that the reconstruction of images in small goaf based on HT-GN algorithm does not rely on iterative initial values, and the image evaluation parameters are superior to Tikhonov algorithm, with better convergence performance, effectively improving the ill posedness of frequency domain electromagnetic imaging inverse problems in small goaf.