Let PR(X) denote the hyperspace of non-empty finite subsets of a topological space X with Pixley–Roy topology. In this paper, we investigate the quasi-Rothberger property in hyperspace PR(X). We prove that for a space X, the followings are equivalent: (1) PR(X) is quasi-Rothberger; (2) X satisfies S 1 (Π rc f −h , Π wrc f −h); (3) X is separable and each co-finite subset of X satisfies S 1 (Π pc f −h , Π wpc f −h); (4) X is separable and PR(Y) is quasi-Rothberger for each co-finite subset Y of X. We also characterize the quasi-Menger property and the quasi-Hurewicz property of PR(X). These answer the questions posted in [8].