We propose and describe a hybrid GRASP with weight perturbations and adaptive path-relinking heuristic (HGP-PR) for the Steiner problem in graphs. In this multi-start approach, the greedy randomized construction phase of a GRASP is replaced by the combination of several construction heuristics with a weight perturbation strategy. A strategic oscillation scheme combining intensification and diversification elements is used for the perturbation of the original weights. The improvement phase circularly explores two different local search strategies: the first uses a node-based neighborhood for local search, while the second uses a key-path-based neighborhood. An adaptive path-relinking technique is applied to a set of elite solutions as an intensification strategy. Computational experiments on a large set of benchmark problems of three different classes are reported. We first illustrate the effectiveness of preprocessing procedures for several classes of test problems. Next, we present computational results illustrating the contribution of each algorithmic feature to the robustness of the complete algorithm. Finally, we compare the hybrid GRASP with perturbations and adaptive relinking algorithm with other heuristics from the literature. The new heuristic HGP-PR outperformed other algorithms, obtaining consistently better or comparably good solutions for all classes of test problems.