The invasive grass Bromus tectorum (cheatgrass, downy brome) has extensive ecological breadth in its introduced range, and is increasing in abundance at high elevations. As a predominantly selfing species with high potential population growth rates, it is a likely candidate for having general-purpose genotypes that facilitate its invasion into high elevations. We evaluated evidence for general-purpose genotypes by examining phenotypic and molecular variation in B. tectorum from low- and high-elevation sites in the Rocky Mountains. Common garden experiments revealed that plants from high elevations germinated faster, but no other phenological, morphological, or physiological differences were found between elevations. Leaf length was longer for low-elevation sites in a common garden using field-collected seeds, but this was not found in a common garden using greenhouse-grown seeds, suggesting maternal effects. For most traits, there was significant phenotypic variation among sites and individuals. Using microsatellites, we genotyped individuals from low- and high-elevation sites. We found no indication of genetic differentiation at these loci between high and low elevations, but there was significant variation within and among sites. No single genotype was common across sites. The success of B. tectorum is not due to a few general-purpose genotypes, but rather many genotypes associated with many different phenotypes. Understanding the mechanisms behind the success of invaders enhances our knowledge of basic evolutionary and ecological processes and is crucial to our ability to manage ongoing, and prevent future, invasions, especially into new habitats.