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Addressing human image matting without trimap is very challenging. The latest methods rely on estimating a segmentation map or a pseudo trimap to constrain the matting process. However, their matting accuracy typically affects by the errors in these auxiliary maps. Motivated by recent flaw correction approaches, we propose a novel neural approach to address this problem: We first train a model to directly compute an initial matte, of which the errors are further detected by a flaw detector and corrected by a refinement process. Our method, named Semantics-Adding Flaw-Erasing network (SAFE-Net), has two novel modules: a Semantic Addition module (SAM) to enrich matting features with human semantics via an attention mechanism and a Flaw Elimination module (FEM) to correct errors in the defective matte regions. To facilitate the learning process, we have further constructed a large human matting dataset containing 4,729 unique foregrounds with fine annotations. Extensive experiments demonstrate that SAFE-Net outperforms existing trimap-free human image matting methods.