Many studies have examined the impact of dispersal on local adaptation, but much less attention has been paid to how local adaptation influences range shifts. The aim of this study was to test how local adaptation might affect climate-driven range shifts in plants, and if this might differ between plants with different life histories. Simulated range shift dynamics were compared for hypothetical annual, perennial and tree species, each comprised of either one plastic genotype or six locally adapted genotypes. The landscape consists of shifting climate bands made up of 20 × 20 m patches containing multiple individuals. Effects of seed dispersal, breadth of the plastic species' tolerance, steepness of the climate gradient and rate of the climate shift are also examined. Local adaptation increased the equilibrium range size and aided range shifts by boosting fitness near range edges. However, when the rate of climate change was doubled on a steep gradient, locally adapted trees exhibited a higher percent loss of range during the climate shift. The plastic annual species with short dispersal was unable to recover its range size even after the climate stabilized, while the locally adapted annuals tracked climate change well. The results suggest that in most situations local adaptation and longer dispersal distances will be advantageous, though not necessarily sufficient, for tracking suitable climates. However, local adaptation might put species with long generation times at greater risk when climate shifts are very rapid. If confirmed by empirical tests, these results suggest that identifying variation between species in how fitness varies along climate gradients and in these key demographic rates might aid in prioritizing management actions.