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Currently, there is a rapidly increasing need for high-quality biomedical knowledge graphs (BioKG) that provide direct and precise biomedical knowledge. In the context of COVID-19, this issue is even more necessary to be highlighted. However, most BioKG construction inevitably includes numerous conflicts and noises deriving from incorrect knowledge descriptions in literature and defective information extraction techniques. Many studies have demonstrated that reasoning upon the knowledge graph is effective in eliminating such conflicts and noises. This paper proposes a method BioGRER to improve the BioKG's quality, which comprehensively combines the knowledge graph embedding and logic rules that support and negate triplets in the BioKG. In the proposed model, the BioKG refinement problem is formulated as the probability estimation for triplets in the BioKG. We employ the variational EM algorithm to optimize knowledge graph embedding and logic rule inference alternately. In this way, our model could combine efforts from both the knowledge graph embedding and logic rules, leading to better results than using them alone. We evaluate our model over a COVID-19 knowledge graph and obtain competitive results.