Abstract: For the target detection of abnormal magnetic signals, the extracted effective features are so weak that they are easily disturbed by a strong background noise, with a great uncertainty for the quality of the measured data. To address this problem, a data-driven sparse feature extraction method based on the tunable Q-factor wavelet transform (TQWT) and the overlapping group shrinkage algorithm is developed in this paper. Compared with the traditional fixed Q-factor wavelet transform, the proposed method is superior in the fact that it allows flexibly tuning the Q-factor according to the oscillation characteristics of the useful features of the signal. In this way, the sparsity of the extracted features can be induced more effectively. In addition, with the overlapping group shrinkage (OGS) algorithm, the weak features from signals with group property can be effectively extracted, to enhance the extraction accuracy of features. Finally, the proposed method is applied to the feature extraction of the magnetic anomaly signal with a case example, which verifies the effectiveness of the method for the magnetic signal target detection.