Despite the significant effect that invasive species have on natural values, the number and extent of invasions continue to rise globally. At least three dominant reasons explain why policy development and implementation can fail: differences in managers' mental models of invasive species management; cross-agency responsibility; and poor planning and management (i.e., planning-implementation gap). We used a case study of cross-agency management of gamba grass (. Andropogon gayanus) in Australia to explore the differences in organizational staffs' mental models of management. The gamba grass invasion in northern Australia is continuing to expand and associated effects are increasing; coordinated action across agencies is needed to manage the expansion. Our aim was to examine how staff would represent their mental models as a diagram that we could compare between individuals and groups. We used cognitive mapping techniques to elicit models of 15 individuals from across 5 organizations, represented as an influence diagram, which shows the interrelationships that define a system. We compiled the individual influence diagrams to create a team model of management that captures the common connections across participants' diagrams. The team model revealed that education, science, legislation, enforcement and property management plans were perceived to be the most important management tools to control or eradicate gamba grass. The Weed Management Branch was perceived to have the most central role in gamba grass management, while other organizations were perceived to have specific roles according to their core business. Significant positive correlations (i.e., shared perceptions) were observed across half of the participants, indicating that the some participants have shared models that could be used as a starting point for discussing the team model, clarifying roles and responsibilities, and potentially building consensus around a shared model. Dominant opportunities for improvement identified by participants were better use of management tools, namely education and enforcement, better coordination and collaboration between agencies and increased resourcing. Our research demonstrates the value and validity of using influence diagrams to explore managers' mental models and to create a team model that could serve as a starting point for improved cross-agency natural resource management.