Recent accelerated trends of human-induced global changes are providing many examples of adaptation to novel environments. Although the rate of environmental change can vary dramatically, its effect on evolving populations is unknown. A crucial feature explaining the adaptation to harsh environments is the supply of beneficial mutations via immigration from a 'source' population. In this study, we tested the effect of immigration on adaptation to increasing concentrations of antibiotics. Using experimental population of Pseudomonas aeruginosa, a pathogenic bacterium, we show that higher immigration rates and a slow increase in antibiotic concentration result in a more rapid evolution of resistance; however, a high immigration rate combined with rapid increases in concentration resulted in higher maximal levels of resistance. These findings, which support recent theoretical work, have important implications for the control of antibiotic resistance because they show that rapid rates of change can produce variants with the ability to resist future treatments.