The rapid invasion of lionfish into the Western North Atlantic and Caribbean will undoubtedly affect native reef fishes via processes such as trophic disruption and niche takeover, yet little is known about the dynamics of this invasion. We constructed a stage-based, matrix population model in which matrix elements were comprised of lower-level parameters. Lionfish vital rates were estimated from existing literature and from new field and laboratory studies. Sensitivity analysis of lower-level parameters revealed that population growth rate is most influenced by larval mortality; elasticity analysis of the matrix indicated strong influence of the adult and juvenile survival elements. Based on this model, approximately 27% of an invading adult lionfish population would have to be removed monthly for abundance to decrease. Hierarchical modeling indicated that this point estimate falls within a broad uncertainty interval which could result from imprecise estimates of life-history parameters. The model demonstrated that sustained removal efforts could be substantially more effective by targeting juveniles as well as adults.