Bromus tectorum (cheatgrass) is an annual Eurasian grass that has invaded rangelands of the western USA. Being both a fire follower and a fire promoter, it can rapidly exclude native vegetation and is among the greatest threats to conservation in the region. Key to land management is a strong understanding of B. tectorum distribution and density. Percentage ground cover of B. tectorum was estimated and mapped as a continuous variable over 13.3millionha in Nevada, USA. Estimation involved a statistical model derived from 262 training plots, two dates of six scenes from Landsat 7 ETM+ imagery collected in 2001, and elevation. Absence of B. tectorum in many plots led to a dataset that was left‐censored at zero for the response variable, B. tectorum ground cover. Tobit regression, a method for modelling censored data, was found to produce a better model from these data than ordinary least squares regression. The two dates of the imagery were used to derive a variable representing phenology of the landscape. The derived phenology (in quadratic form), elevation, and the late‐season green band were statistically significant in the model development. Additionally, a brightness index was used to limit estimates in bright and dark portions of the imagery such as playas and lakes. Final map accuracy determined from an additional 75 independent assessment plots showed good correspondence between sampled and estimated B. tectorum ground cover ( r = 0.71) and the root‐mean‐square error for estimated ground cover is 9.1%.