As an emerging technology, device-free localization (DFL) using wireless sensor networks to detect targets not carrying any electronic devices, has spawned extensive applications, such as security safeguards and smart homes or hospitals. Previous studies formulate DFL as a classification problem, but there are still some challenges in terms of accuracy and robustness. In this paper, we exploit a generalized thresholding algorithm with parameter p as a penalty function to solve inverse problems with sparsity constraints for DFL. The function applies less bias to the large coefficients and penalizes small coefficients by reducing the value of p. By taking the distinctive capability of the p thresholding function to measure sparsity, the proposed approach can achieve accurate and robust localization performance in challenging environments. Extensive experiments show that the algorithm outperforms current alternatives.