Invasive species pose a serious risk to the biological, cultural and economic value of marine ecosystems. In an increasingly connected world, maritime traffic has become a key driver of this risk, with vessels transporting species between domestic and international locations. Network models are a useful technique for characterizing connectivity in transport systems, and subsequent risk of invasion through these connections. Using New Zealand as a case study, we have developed a decision-support tool to simulate the spread of marine invasive species under different incursion and management scenarios. This process-based network model estimates relative incursion risk to domestic ports and other locations over time, combining the influence of commercial, recreational and aquaculture vessels with species growth, in-transit mortality and recruitment rates. It tracks the flow of potential propagule pressure through the invasion sub-processes of entrainment, transport, introduction, establishment and population growth. We undertook global sensitivity analysis of the biological parameters using Sobol indices and boosted regression trees, and found the parameters produced plausible outcomes within the specified value ranges. Our simulation results can be used to direct the location, type and magnitude of biosecurity intervention in New Zealand, and this approach could be adapted to other locations and scales.