The potential distribution of alien species in a novel habitat often is difficult to predict because factors limiting species distributions may be unique to the new locale. Eragrostis lehmanniana is a perennial grass purposely introduced from South Africa to Arizona, USA in the 1930s; by the 1980s, it had doubled its extent. Based on environmental characteristics associated with its introduced and native range, researchers believed that E. lehmanniana had reached the limits of its distribution by the early 1990s. We collected data on E. lehmanniana locations from various land management agencies throughout Arizona and western New Mexico and found new records that indicate that E. lehmanniana has continued to spread. Also, we employed two modelling techniques to determine the current potential distribution and to re-investigate several environmental variables related to distribution. Precipitation and temperature regimes similar to those indicated by past research were the most important variables influencing model output. The potential distribution of E. lehmanniana mapped by both models was 71,843 km2 and covers a large portion of southeastern and central Arizona. Logistic regression (LR) predicted a potential distribution of E. lehmanniana more similar to this species current distribution than GARP based on average temperature, precipitation, and grassland species composition and recorded occurrences. Results of a cross-validation assessment and extrinsic testing showed that the LR model performed as well or better than GARP based on sensitivity, specificity, and kappa indices.