In this paper, we introduce and study the concept of \(\Sigma \) -dual-Rickart modules which is the dual case of \(\Sigma \) -Rickart modules. An A-module X is said to be a \(\Sigma \) -dual-Rickart if every direct sum of copies of X is a dual-Rickart module. We show when a \(\Sigma \) -Rickart module is a \(\Sigma \) -dual-Rickart module and vice-versa. Also, we characterize semisimple Artinian rings, regular rings, semi-hereditary rings, cohereditary modules and FP-injective modules in terms of \(\Sigma \) -dual-Rickart modules. Further, we study the endomorphism ring of a \(\Sigma \) -dual-Rickart module.