Multi-frequency electrical impedance tomography (mfEIT) offers a nondestructive imaging technology that reconstructs the distribution of electrical characteristics within a subject based on the impedance spectral differences among biological tissues. However, the technology faces challenges in imaging multi-class lesion targets when the conductivity of background tissues is frequency-dependent. To address these issues, we propose a spatial-frequency cross-fusion network (SFCF-Net) imaging algorithm, built on a multi-path fusion structure. This algorithm uses multi-path structures and hyper-dense connections to capture both spatial and frequency correlations between multi-frequency conductivity images, which achieves differential imaging for lesion targets of multiple categories through cross-fusion of information. According to both simulation and physical experiment results, the proposed SFCF-Net algorithm shows an excellent performance in terms of lesion imaging and category discrimination compared to the weighted frequency-difference, U-Net, and MMV-Net algorithms. The proposed algorithm enhances the ability of mfEIT to simultaneously obtain both structural and spectral information from the tissue being examined and improves the accuracy and reliability of mfEIT, opening new avenues for its application in clinical diagnostics and treatment monitoring.