Given a graph \(G=(V,E)\) and a subset \(S \subseteq V(G)\) , the Subset Feedback Vertex Set (SFVS) problem asks to find a minimum vertex set that intersects every cycle containing a vertex from set S. SFVS is known to be NP-hard on general graphs. The computational complexity of SFVS on AT-free graphs was posed as an open problem by Papadopoulos et al. in [25]. We resolve this problem by presenting a polynomial-time algorithm for SFVS on AT-free graphs. Along with this, we also present a polynomial time algorithm for Subset Vertex Cover (SVC) problem on AT-free graphs. In SVC, the task is to find a minimum vertex set that contains an endpoint of every edge which contains some vertex from S as its end point. We note here, SVC is used as a subroutine to compute SFVS.