The Group Steiner Tree Problem (GSTP) is widely used in graph data management and mining, yet existing algorithms trade off practical efficiency against approximation quality: efficient methods offer only linear guarantees, while those with sublinear guarantees fail to scale to large graphs. In this paper, we present MonoGST+, a novel algorithm for GSTP that breaks this trade‑off by achieving a sublinear approximation while matching the running time of state‑of‑the‑art linear‑approximation solvers. Our approach extends a 2‑star‑based reduction to weighted set cover with a suspendable search and a monotonicity‑ and unimodality‑aware pruning strategy to eliminate redundant computation. Experiments on multiple real‑world datasets demonstrate the effectiveness and efficiency of MonoGST+, providing a practical, high‑quality solution for GSTP applications.