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In this short note we are concerned with the Kahler-Einstein metrics nearcone type log canonical singularities. By two different approaches, weconstruct a complete Kahler-Einstein metric with negative scalar curvature in aneighborhood of the cone over a Calabi-Yau manifold, which provides a localmodel for the future study of the global Kahler-Einstein metrics on singularvarieties. In the first approach, we show that the singularity is uniformizedby a complex ball and hence the induced metric from the Bergman metric of theball is a desired one. In the second approach, we obtain a completeKahler-Einstein metric with negative curvature by using Calabi Ansatz. At last,we show that these two metrics are indeed the same.

On the construction of a complete Kahler-Einstein metric with negative scalar curvature near an isolated log-canonical singularity