Humans are facilitating the introduction and range expansion of invasive alien species (IAS), which have negatively impacted ecological and socio-economic systems worldwide. Understanding the global diffusion of IAS is important for developing environmental policies and management strategies. We estimate the rate of increase and the doubling times of the number of new records of 178 IAS using a global dataset with c. 3.4 million records obtained over c. 100 years. Here, we show that the number of records of IAS have exponentially increased with a mean double time of c. 14 years across the Earth. For the most analysed species, the number of records increased faster in the non-native than native continents, suggesting that such IAS might be exponentially expanding their range size. We also found that each continent has a taxonomic group with a particular increase in IAS records. Governments and scientists should pay attention to these taxonomic groups to implement appropriate control or management actions. Our study provides an indication that the current local, regional and continental efforts to control invasions may be not sufficient at the global scale. This is a concerning situation given the great number of areas available for invasion worldwide.