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In this paper we present the Ricci curvature on cell-complexes and show theGauss-Bonnnet type theorem on graphs and 2-complex that decomposes closedsurface. The defferential forms on a cell complex is defined as linear maps onchain complex, and Laplacian operates this defferential forms. Then weconstruct the Bochner-Weitzenb\"ock formula and define the Ricci curvature.This curvature is determined by the combinatorial calculation. We show also theproperties of combinatorial vector fields on a cell complex

Combinatorial Ricci curvature on cell-complex and Gauss-Bonnnet Theorem