Site-specific weed management (on the scale of a few meters or less) has the potential to greatly reduce pesticide use and its associated environmental and economic costs. A prerequisite for site-specific weed management is the availability of accurate maps of the weed population that can be generated quickly and cheaply. Improvements and cost reductions in unmanned aerial vehicles (UAVs) and camera technology mean these tools are now readily available for agricultural use. We used UAVs to collect aerial images captured in both RGB and multispectral formats of 12 cereal fields (wheat [Triticum aestivum L.] and barley [Hordeum vulgare L.]) across eastern England. These data were used to train machine learning models to generate prediction maps of locations of black-grass (Alopecurus myosuroides Huds.), a prolific weed in UK cereal fields. We tested machine learning and data set resampling methods to obtain the most accurate system for predicting the presence and absence of weeds in new out-of-sample fields. The accuracy of the system in predicting the absence of A. myosuroides is 69% and its presence above 5 g in weight with 77% accuracy in new out-of-sample fields. This system generates prediction maps that can be used by either agricultural machinery or autonomous robotic platforms for precision weed management. Improvements to the accuracy can be made by increasing the number of fields and samples in the data set and the length of time over which data are collected to gather data across the entire growing season.