Long-distance seawater intrusion has been widely observed through the subsurface conduit system in coastal karst aquifers as a source of groundwater contaminant. In this study, seawater intrusion in a dual-permeability karst aquifer with conduit networks is studied by the two-dimensional density-dependent flow and transport SEAWAT model. Local and global sensitivity analyses are used to evaluate the impacts of boundary conditions and hydrological characteristics on modeling seawater intrusion in a karst aquifer, including hydraulic conductivity, effective porosity, specific storage, and dispersivity of the conduit network and of the porous medium. The local sensitivity analysis evaluates the parameters' sensitivities for modeling seawater intrusion, specifically in the Woodville Karst Plain (WKP). A more comprehensive interpretation of parameter sensitivities, including the nonlinear relationship between simulations and parameters, and/or parameter interactions, is addressed in the global sensitivity analysis. The conduit parameters and boundary conditions are important to the simulations in the porous medium because of the dynamical exchanges between the two systems. The sensitivity study indicates that salinity and head simulations in the karst features, such as the conduit system and submarine springs, are critical for understanding seawater intrusion in a coastal karst aquifer. The evaluation of hydraulic conductivity sensitivity in the continuum SEAWAT model may be biased since the conduit flow velocity is not accurately calculated by Darcy's equation as a function of head difference and hydraulic conductivity. In addition, dispersivity is no longer an important parameter in an advection-dominated karst aquifer with a conduit system, compared to the sensitivity results in a porous medium aquifer. In the end, the extents of seawater intrusion are quantitatively evaluated and measured under different scenarios with the variabilities of important parameters identified from sensitivity results, including salinity at the submarine spring with rainfall recharge, sea level rise, and a longer simulation time under an extended low rainfall period.