A space X is star-K-Menger if for each sequence (Un : n ∈ N) of open covers of X there exists a sequence (Kn : n ∈ N) of compact subsets of X such that {St(Kn, Un) : n ∈ N} is an open cover of X. In this paper, we investigate the relationship between star-K-Menger spaces and related spaces, and study topological properties of star-K-Menger spaces.