Magnetic particle imaging (MPI) is an emerging preclinical tomography technology with high resolution and sensitivity. However, MPI reconstruction artifacts affect the imaging accuracy and quality, which may lead to misdiagnosis or missed diagnosis of disease. In this study, a modified reconstruction method of MPI is proposed, which is called non-negative weighted least absolute shrinkage and selection operator (LASSO) regularization (NWLR). After the reconstruction based on NWLR, the image post-processing of calibration based on normalized cross-correlation (NCC) and artifact suppression based on the deep image prior (DIP) are conducted to further improve the reconstruction quality. To demonstrate the advantages of the proposed method, the reconstruction result is compared with other three popular methods with respect to both visualization and performance indexes. The results show that the proposed NWLR method yields fewer artifacts and higher accuracy than the other three methods. Furthermore, the PSNR and SSIM are improved by 13.73% and 20.10% through post-processing, respectively. The NRMSE of the proposed NWLR–NCC–DIP method is decreased by 32.07%. The conducted studies demonstrate that the NWLR–NCC–DIP method proposed in this study achieves better reconstruction performance than the other popular methods. The reconstruction quality and accuracy are improved rapidly, which is of great practical importance for its preclinical applications.