Because of the large number of potentially invasive species, and the time required to complete weed risk assessments (WRAs) with the use of the current, mandated system in the United States, species need to be prioritized for assessment and possible listing as Federal Noxious Weeds. Our objective was to rank the potential invasiveness of weedy or pest plant species not yet naturalized in the United States. We created a new model of invasiveness (hereafter the U.S. weed-ranking model) based on scoring factors within four elements: (1) invasiveness potential, or likelihood to exhibit invasive behavior; (2) geographic potential, or habitat suitability; (3) damage potential, or likely impact; and (4) entry potential, or likelihood to be introduced. The ranking score was the product of the four elements. We scored 250 species satisfactorily, from a list of 700 +. We analyzed model sensitivity to scoring factors, and compared results to those from a WRA model for Hawaii. For species not in cultivation in the United States, the top 25 species included a mix of annuals, perennials, sedges, shrubs, and trees. Most had exhibited invasive behavior in at least several other countries. Because of greater entry potential scores, the highest-scoring species were weeds in cultivation. Twenty-nine such species, out of 44 total, had scores greater than the highest scoring species not in cultivation. In comparison to the Hawaii WRA model, correlation and regression analyses indicated that the U.S. weed-ranking model produced similar, but not exact, results. The ranking model differs from other WRAs in the inclusion of entry potential and the use of a multiplicative approach, which better suited our objectives and United States regulations. Two highly ranked species have recently been listed as Federal Noxious Weeds, and we expect most top-tier species to be similarly assessed.