Lehmann lovegrass (Eragrostis lehmanniana), an invasive grass dominating many grassland sites in the Sonoran Desert, has had a limited distribution in the Chihuahuan Desert. Climate (precipitation and temperature) is suggested to be the main driver for the difference in the current spatial distributions of the species in the two deserts. Our goal was to predict the distribution of Lehmann lovegrass throughout the Chihuahuan Desert under current climate conditions and future climate scenarios. We used the SOILWAT model to simulate Lehman lovegrass seedling establishment at > 60 locations in the US portion of the Chihuahuan Desert. We then extrapolated the results to the entire region by using the 1981-2010 mean precipitation and temperature data from PRISM and the soil data from the SSURGO database. Future climate conditions were adjusted as follows: daily temperature was increased by 2.5 oC, and daily precipitation was increased or decreased by 5 and 10%. Our results showed that the simulated distribution of Lehmann lovegrass in the Chihuahuan Desert under current climatic conditions is mainly in the southern part of the region, similar to the observed distribution. The spatial distribution under future climate scenarios varies due to the combined effects of precipitation and temperature. The species distribution contracts when precipitation decreases 5 or 10% or daily temperature increases 2.5 oC. The species distribution expands when temperature stays the same and precipitation increases 5 and 10%. Our study shows that the distribution of Lehmann lovegrass in the Chihuahuan Desert will depend on the amount and direction of changes in future temperature and precipitation. This uncertainty in the projected distribution adds one more challenge to land management of this invasive grass under climate change.