In this paper, the notions of countable S∗-compactness is introduced in L-topological spaces based on the notion of S∗-compactness. An S∗-compact L-set is countably S∗-compact. If L = [0, 1], then countable strong compactness implies countable S∗-compactness and countable S∗-compactness implies countable F-compactness, but each inverse is not true. The intersection of a countably S∗-compact L-set and a closed L-set is countably S∗-compact. The continuous image of a countably S∗-compact L-set is countably S∗-compact. A weakly induced L-space (X, T ) is countably S∗-compact if and only if (X, [T ]) is countably compact.