In this talk, we care about a sequence of Riemannian embeddings in a closed 3-manifold, with uniformly bounded genus and area, whose Willmore functional values turning to zero. We prove such a sequence will converges to a minimal embedding with finite multiplicities outside a finite set of singular points.  The convergence is in the sense of both intrinsic L^p_{loc} convergence and extrinsic weak W^{2,2} convergence introduced in [SZ]. And the singularities of the limit embedding map are removable thanks to the convergence outside the singular points is W^{1,p}_{loc} for any p>1, which is stronger than C^0_{loc}.