Plant-pollinator-robber systems are considered, where the plants and pollinators are mutualists, the plants and nectar robbers are in a parasitic relation, and the pollinators and nectar robbers consume a common limiting resource without interfering competition. My aim is to show a mechanism by which pollination-mutualism could persist when there exist nectar robbers. Through the dynamics of a plant-pollinator-robber model, it is shown that (i) when the plants alone (i.e., without pollination-mutualism) cannot provide sufficient resources for the robbers' survival but pollination-mutualism can persist in the plant-pollinator system, the pollination-mutualism may lead to invasion of the robbers, while the pollinators will not be driven into extinction by the robbers' invasion. (ii) When the plants alone cannot support the robbers' survival but persistence of pollination-mutualism in the plant-pollinator system is density-dependent, the pollinators and robbers could coexist if the robbers' efficiency in translating the plant-robber interactions into fitness is intermediate and the initial densities of the three species are in an appropriate region. (iii) When the plants alone can support the robbers' survival, the pollinators will not be driven into extinction by the robbers if their efficiency in translating the plant-pollinator interactions into fitness is relatively larger than that of the robbers. The analysis leads to an explanation for the persistence of pollination-mutualism in the presence of nectar robbers in real situations.