Several freshwater mussel species represent some of the most problematic invasive species and have considerably altered ecosystems worldwide. Their invasion potential has been partially attributed to their free-living larvae, which have a high dispersal capability. We investigated the invasion potential of Anodonta (Sinanodonta) woodiana, a species of East Asian unionid mussel established worldwide despite having an obligatory parasitic stage (glochidium), which must encyst on host fish. The invasion success of A. woodiana has been attributed to the success of worldwide introductions of its sympatric fish hosts. We experimentally found, however, that A. woodiana is a broad host generalist, which can complete its development on all eight fish species tested, both coinvasive and native. Subsequently, we used a data on the occurrence and relative abundance of potential hosts in river habitats in the Czech Republic to project scenarios of the effect of host availability on A. woodiana invasion. We found that host availability does not constitute a major limit for A. woodiana to colonise most aquatic habitats in Central Europe. In addition, we investigated seasonal dynamics of A. woodiana reproduction and did not detect any limitations of its reproduction by ambient water temperatures typical of a Central European lowland river. Consequently, we predict that A. woodiana may further increase the speed and range of its invasion and we discuss possible consequences to native habitats and communities, especially to the endangered species of unionid mussels.