We have analyzed the effects of a simple wormhole, known as the Ellis–Bronnikov-type wormhole, on a scalar field, where, analytically, we determine solutions of bound states and show that the relativistic energy profile of this scalar field is drastically influenced by the topology of space-time characterized by the presence of a global monopole. Before this analysis, we investigated the effects of this background on the deflection of light, which is influenced by the parameters associated with the wormhole throat and the topological defect.