A general prediction of ecological theory is that climate change will favor invasive nonindigenous plant species (NIPS) over native species. However, the relative fitness advantage enjoyed by NIPS is often affected by resource limitation and potentially by extreme climatic events such as drought. Genetic constraints may also limit the ability of NIPS to adapt to changing climatic conditions. In this study, we investigated evidence for potential NIPS advantage under climate change in two sympatric perennial stipoid grasses from southeast Australia, the NIPS Nassella neesiana and the native Austrostipa bigeniculata. We compared the growth and reproduction of both species under current and year 2050 drought, temperature and CO2 regimes in a multifactor outdoor climate simulation experiment, hypothesizing that NIPS advantage would be higher under more favorable growing conditions. We also compared the quantitative variation and heritability of growth traits in populations of both species collected along a 200 km climatic transect. In contrast to our hypothesis we found that the NIPS N. neesiana was less responsive than A. bigeniculata to winter warming but maintained higher reproductive output during spring drought. However, overall tussock expansion was far more rapid in N. neesiana, and so it maintained an overall fitness advantage over A. bigeniculata in all climate regimes. N. neesiana also exhibited similar or lower quantitative variation and growth trait heritability than A. bigeniculata within populations but greater variability among populations, probably reflecting a complex past introduction history. We found some evidence that additional spring warmth increases the impact of drought on reproduction but not that elevated atmospheric CO2 ameliorates drought severity. Overall, we conclude that NIPS advantage under climate change may be limited by a lack of responsiveness to key climatic drivers, reduced genetic variability in range-edge populations, and complex drought-CO2 interactions.