While an accurate image reconstruction of digital breast tomosynthesis (DBT) is fundamentally impossible due to its limited data, the DBT is increasingly used in clinics for its rich image information at a relatively low dose. One of the dominant image artifacts in DBT that hinders a faithful diagnosis is high-density object artifact in conjunction with a limited angle problem. In this paper, we developed a very efficient method for reconstructing DBT images with much reduced high-density object artifacts. The method is based on backprojection filtration reconstruction algorithm, voting strategy, and image blending. Data derivatives were backprojected with appropriate weights to reduce ripple artifacts by use of the voting strategy. We generated another differentiated backprojection volume, where the edges of high-density objects are replaced by the background. After Hilbert transform, we blended the two images to reduce undershoot artifacts. Physical phantoms were scanned and we compared conventional filtered backprojection, filtered backprojection with weighted backprojection, and our proposed method. Ripple artifacts were dramatically suppressed and undershoot artifacts were also greatly suppressed in the proposed method.