Due to ongoing climate change and the spread of invasive pests, understanding and predicting climatic suitability for invasive insect species has shown growing demand from government and industry biosecurity managers. The invasive pest Bactericera cockerelli, (Šulc) (Hemiptera: Triozidae), commonly known as tomato potato psyllid (TPP), is native to North America and has recently invaded Australasia. TPP is also the vector of the bacterial plant pathogen Candidatus Liberibacter solanacearum (CLso), which has caused severe economic losses for potato growers worldwide. We used the niche modelling software CLIMEX to predict the potential geographical distribution of TPP in Australasia and worldwide under current and future climatic scenarios. Our model prediction of the current climate conditions closely agrees with all the known distributions of TPP. In its native range (North America), TPP is predicted to expand its current geographical range in semi‐arid, temperate, and continental climates. Within Australia, along with the known occurrence of TPP in Western Australia, potential expansion into South Australia, Victoria, New South Wales and Queensland is predicted. The predicted distribution closely matches all the known records with higher climatic suitability in New Zealand. Globally, the model projected that the pest‐free countries in Europe and East Asia are climatically more suitable for TPP. Predictions under the future climate change scenarios (A1B, CSIRO Mk 3.0 for 2090) showed a significant reduction of the known geographical range of TPP with a possible expansion towards higher latitudes. Areas in North America and Australia are projected to be less climatically suitable for the survival of TPP in future climates. However, our model suggested that Europe and New Zealand will remain unchanged or will become more favourable in the future. These CLIMEX projections for current and future climatic distribution provide valuable information for existing and future biosecurity preparedness and management programmes, which may prove helpful in risk assessments and identifying potential areas that are likely to be susceptible to a TPP invasion.