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The Max-Cover is a NP-hard problem. Therefore, the heuristic approach is suitable to solve this problem for large instances. Quantum annealing is a heuristic quantum optimization algorithm that can be used to handle the Max-Cover problem. Recent developments in quantum technology allows creating programmable quantum processors to implement the quantum annealing technique. In this article, we apply the quantum annealing approach to solve the Max-Cover problem. The experimental results show that this approach gives better results than Simulated Annealing in terms of both solution quality and annealing time.