Abstract Knowledge graph embedding aims at offering a numerical knowledge representation paradigm by transforming the entities and relations into continuous vector space. However, existing methods could not characterize the knowledge graph in a fine degree to make a precise link prediction. There are two reasons for this issue: being an ill-posed algebraic system and adopting an overstrict geometric form. As precise link prediction is critical for knowledge graph embedding, we propose a manifold-based embedding principle (ManifoldE) which could be treated as a well-posed algebraic system that expands point-wise modeling in current models to manifold-wise modeling. Extensive experiments show that the proposed models achieve substantial improvements against the state-of-theart baselines, particularly for the precise prediction task, and yet maintain high efficiency.