Shaft-rate electromagnetic (EM) field is a critical feature in the detection of ships and underwater vehicles. However, the signal-to-noise ratio of the shaft-rate EM field is greatly reduced due to the presence of the static EM field, whose main energy is concentrated in the low-frequency section. In order to realize the effective detection of the weak shaftrate EM field signals under a low signal-to-noise ratio, we propose a signal extraction method based on the Adaptive Fourier Decomposition (AFD) algorithm. At the decomposition stage, we utilize the Nevanlinna factorization and the maximal selection principle in each step, and then iteratively obtain various single components from low-frequency to high-frequency. At the extraction stage, the low-frequency information of the signal is effectively reconstructed by summing the first few components, leading to the retrieval of the shaft-rate EM field signal through residual operations. The experiment results on both synthesized and measured data show that the proposed algorithm converges faster with higher fidelity compared to the existing state-of-the-art method.