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The graphical Steiner tree problem is a classical combinatorial optimization problem that appears in many practically important applications. This paper presents a new parallel genetic algorithm for solving the problem. The presented algorithm is based on binary encoding, used the Distance Network Heuristic for evaluating fitness of individuals and is implemented in parallel using global population model. The results of experiments on the OR-Library tests are reported to show the algorithmpsilas performance in comparison with other metaheuristics for the given problem. The speed-up of the parallel implementation is also discussed.