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