An eddy-resolving free-surface primitive-equation model with nonlinear terrain-following coordinates is established to study the exchange of water masses among the Asian marginal seas and their adjacent waters. A curvilinear coordinate system is used to generate the horizontal grid with a variable resolution for the regional oceans from $5^{circ}$S to $45^{circ}$N and $100^{circ}$E to $155^{circ}$E. The higher resolution region has about a 10 km by 10 km grid covering the complex geometry of the coastal marginal seas, while the lower resolution region has about a 30 km by 30 km grid covering the eastern Pacific. The model is initialized by the Levitus annual climitology and forced by the monthly mean air-sea fluxes of momentum, heat, and freshwater derived from the Comprehensive Ocean-Atmosphere Data Set. High-resolution and low-viscosity are identified as the key factors for a better representation of the exchange of waters through narrow straits and passages between the marginal seas and their adjacent waters. The dynamics of the loop currents and eddies in the South China Sea and Celebes Sea are examined in detail. It has found that the anticyclonic loop and detached eddies from the Kuroshio through the Luzon Strait play an important role in transporting warm and salty water into the South China Sea, while the cyclonic circulation of the Mindanao Current in the Celebes Sea plays a role in contributing cold water to the Indonesian throughflow. The deep undercurrent of the western Pacific is shown to provide fresher water to the South China Sea and Celebes Sea. These modeling results suggest that the exchange processes via the narrow straits and passages are of fundamental importance to the maintenance of water masses for the marginal sea region.