In order to study the flat and cotorsion property of modules, the notion of strongly cotorsion dimension is introduced. It is proved that over a non-coherent ring, there exists a module whose strongly cotorsion dimension is strictly greater than its cotorsion dimesion, and some characterizations of the finiteness of global strongly cotorsion dimension of rings are given. This finiteness will provide some new thoughts to study the coincidence of the Gorenstein projective and Gorendtein AC-projective modules.