The tiger mosquito Ae. albopictus is a species indigenous to the oriental region, but it is now widespread in many countries throughout the world. It is an aggressive mosquito, which causes nuisance and it is well known as an important disease vector. It is one of the world’s most invasive species and is now invading Europe by both natural means and human assisted dispersal. There is no a common view on the limit of the area of potential distribution of the tiger mosquito in Europe, and the role of the environmental driving variable, mainly temperature, in determining the spatial variation of the potential population abundance of the mosquito has not been adequately investigated. To assess the risk posed by Ae. albopictus to Europe a lattice model based on temperature-dependent physiologically based demographic modelling approach has been developed and validated with field observations. The area of potential distribution of this insect is simulated in light of the current climate and climate change scenarios. An index of population abundance is derived in order to investigate the average annual abundance as well as the change in the pattern of population dynamics as function of the local climatic conditions. Uncertainties associated with model parameter variability are considered to support the reliability of model results.