In this paper, a new notion of sequential compactness is introduced in L-topological spaces, which is called sequentially S?-compactness. If L = [0, 1], sequential ultra-compactness, sequential N-compactness and sequential strong compactness imply sequential S?-compactness, and sequential S?-compactness implies sequential F-compactness. The intersection of a sequentially S?-compact L-set and a closed L-set is sequentially S?-compact. The continuous image of an sequentially S?- compact L-set is sequentially S?-compact. A weakly induced L-space (X, T ) is sequentially S?-compact if and only if (X, [T ]) is sequential compact. The countable product of sequential S?-compact L-sets is sequentially S?-compact.