A non-native plant species spreading along an environmental gradient may need to adjust its growth to the prevailing conditions that it encounters by a combination of phenotypic plasticity and genetic adaptation. There have been several studies of how non-native species respond to changing environmental conditions along latitudinal gradients, but much less is known about elevational gradients. We conducted a climate chamber experiment to investigate plastic and genetically based growth responses of 13 herbaceous non-native plants along an elevational gradient from 100 to 2,000 m a. s. l. in Tenerife. Conditions in the field ranged from high anthropogenic disturbance but generally favourable temperatures for plant growth in the lower half of the gradient, to low disturbance but much cooler conditions in the upper half. We collected seed from low, mid and high elevations and grew them in climate chambers under the characteristic temperatures at these three elevations. Growth of all species was reduced under lower temperatures along both halves of the gradient. We found consistent genetically based differences in growth over the upper elevational gradient, with plants from high-elevation sites growing more slowly than those from mid-elevation ones, while the pattern in the lower part of the gradient was more mixed. Our data suggest that many non-native plants might respond to climate along elevational gradients by genetically based changes in key traits, especially at higher elevations where low temperatures probably impose a stronger selection pressure. At lower elevations, where anthropogenic influences are greater, higher gene flow and frequent disturbance might favour genotypes with broad ecological amplitudes. Thus the importance of evolutionary processes for invasion success is likely to be context-dependent.