Abstract Climate data and distribution data for the Canadian waterweed Elodea canadensis Michx. from North America, whole Europe and Finland were used to investigate the ability of bioclimatic envelope models to predict the distribution range and recent northward range shift of the species in Europe. Four different main types of models were developed using the North American data, including either three ‘baseline’ climate variables (growing degrees days, temperature of the coldest month, water balance) or an extended set of seven climate variables, both averaged either over a 30 year time slice or a longer 90 year time slice. Ten different random selections of pseudo-absences were generated from the North American data, on the basis of which ten separate generalized additive models (GAMs) were developed for each main model type. All the 40 developed GAMs were applied first to North America and then transferred to whole Europe and Finland. All the models showed a statistically highly significant accuracy in the three study areas. Although the differences among the four main model types were only minor, the two extended model types showed on average statistically better performance than the two baseline models based on Bayesian information criterion (BIC) values, the amount of deviance explained by the models, resubstitution validation and four-fold cross-validation in North America. They also provided slightly more accurate predictions of climatically suitable area for Elodea canadensis in Finland both in 1961–1984 and 1985–2006. However, the projections from the individual extended models were more variable than projections from the baseline models. Thus model predictions based on a variety of predictor variables but only one selection of pseudoabsences may be subject to biases, and outputs from multiple models should be investigated to better account for uncertainties in modelling. Overall, our results suggest that more attention should be paid to the careful selection of predictor variables and the use of multiple pseudo-absence sets in the ecological niche modelling in order to increase the reliability of the projections of the range shifts of invasive species.