The round goby, an invasive fish from the Black and Caspian Seas, has spread to Swedish waters, threatening recreational fisheries. We modeled impacts on the future recreational fishery in Sweden using data from a recreational fishing survey, and estimated effects of the round goby on other fish species. Values attached to recreational fishing were estimated using a travel cost approach. Catch and consumer surplus were compared before and after a 10-year increase in round goby abundance. Overall impacts of a 10-year increase in round goby abundance in Swedish waters would reduce the present value of consumer surplus by SEK 379-million (EUR 33-million). Any management action keeping a status quo in round goby impact with a price less than about 3 million EUR yearly would hence be justified. This study highlights how aquatic invasive species can cause substantial social losses and that proactive management may be cost-efficient.