Let \({\mathbb{C}}\) be the field of complex numbers (or any algebraically closed field of zero characteristic), V an n-dimensional \({\mathbb{C}}\)-space and \(G=G(k,V)\) the Grassmannian of k-dimensional subspaces of V. The author describes the derived category \(D^ b_{coh}(G)\) of coherent sheaves on G. The main results asserts that \(D^ b_{coh}(G)\) is equivalent with the triangulated category of homotopical category of bounded complexes of graduated \(\bigwedge (V^*)\)-modules, consisting of finite coproducts of modules \(M_{\alpha}\). The modules \(M_{\alpha}\) are canonical associated to Young’s diagrams \(\alpha\) with at most k-rows and most n-k-columns.