In this paper, a new homological Dimension of modules, co-presented Dimension, is defined. We study some basic properties of this homological Dimension. Some ring extensions are considered, too. For instance, we prove that if S R is a finite normalizing extension and SR is a projective module, then for each right S-module MS, the cop-resented Dimension of MS does not exceed the copresented Dimension of HomR(S, M).