Male and female pollinators often exhibit sex-specific preferences for visiting different flowers. Recent studies have shown that these preferences play an important role in shaping the network structure of pollination mutualism, but little is known about how they can mediate plant-plant interactions and population dynamics of competing plants. Inter-plant competition occurs not only directly (e.g. for nutrients, water, and habitats) but also indirectly through pollination. The ecological consequences of sex-specific pollination can be complex. For example, a plant favoured by female pollinators contributes to the production of male pollinators, who may prefer visiting other competing plants and intensify the negative effects of inter-plant competition. Here, we analysed a simple two-plant-one-pollinator model with the sex structure of the pollinator. We observed that (i) sex-specific pollination can have complex consequences for inter-plant competition and coexistence (e.g. the occurrence of non-trivial alternative stable states in which one plant excludes or coexists with the other depending on the initial conditions), (ii) male and female pollinators have distinct ecological consequences because female pollinators have a demographic impact owing to reproduction, and (iii) plants are likely to coexist when male and female pollinators prefer different plants. These results suggest that sex-specific pollination is crucial for competition and coexistence of co-flowering plants. Future, pollination research therefore should more explicitly consider the sex-specific behaviour of pollinating animals.