The shrub Spiraea tomentosa is native to North America and has been domesticated in Europe, where it is now considered an invasive species. The aim of this study was to determine the locations of current suitable climatic niches for this shrub and to estimate future spatial changes in their locations using ecological niche modelling tools. Model results showed that S. tomentosa has large potential natural and secondary ranges, much larger than the range estimated using presence data only. The potential modelled current distribution of S. tomentosa in North America included areas with a relatively humid climate and corresponded with its climate envelope, but in Eurasia, favourable climatic conditions for the shrub occurred in a much larger area than indicated by its current invasive range, so the shrub has not realised its potential climatic niche. Species distribution in its secondary range seems to be random, which may indicate that its true dispersal capacity in Eurasia has not yet been realised. The models showed that climate changes could alter the distribution of the suitable climatic niches available for S. tomentosa, and favour its continuing spread. The shrub could retain the majority of its currently occupied positions in both natural and secondary ranges and simultaneously extend its latitudinal range towards the west in North America and towards the east in Eurasia. In the case of its longitudinal distribution, there may be a shift in the available climate niches to the north, mainly to Scandinavia, and to the south, pushing the shrubs towards mountainous areas with a colder climate. As both current and forecasted future climate conditions seem to favour the consolidation of S. tomentosa populations as well as the extension of its second range in Eurasia, appropriate management strategies should limit or prevent further invasion. It is crucial to limit the intentional and accidental transfer of the shrub, heighten vigilance to identify and eradicate new invasion foci, identify and implement appropriate control techniques and raise public awareness of the invasion threat posed by the species.