Aspace X is said to have the absolutely strongly star --Hurewicz (ASSH) property if for each sequence (𝒰n : n ∈ )of opencovers of X and each dense subset Y of X, there is a sequence (Fn : n ∈ ) of finite subsets of Y such that for each x ∈ X, {n ∈ : x ∉ St(Fn, 𝒰n)}∈ , where is the proper admissible ideal of . In this paper, we investigate the relationship between the ASSH property and other related properties and study the topological properties of the ASSH property. This paper generalizes several results of Song [25] to the larger class of spaces having the ASSH properties.