This article introduces the concept of S-2-absorbing primary submodule as a generalization of 2-absorbing primary submodule. Let S be a multiplicatively closed subset of a ring R and M an R-module. A proper submodule N of M is said to be an S-2-absorbing primary submodule of M if (N : R M) ∩ S = φ and there exists a fixed element s ∈ S such that whenever abm ∈ N for some a, b ∈ R and m ∈ M, then either sam ∈ N or sbm ∈ N or sab ∈ (N : R M). We give several examples, properties and characterizations related to the concept. Moreover, we investigate the conditions that force a submodule to be S-2-absorbing primary.