Global river models are an essential tool for both earth system studies and water resources assessments. As advanced physical processes have been implemented in global river models, increasing computational cost has become problematic for executing ensemble or long-term simulations. To improve computational efficiency, we here propose the use of a local inertial flow equation combined with a vector-based river network map. A local inertial equation, a simplified formulation of the shallow water equations, was introduced to replace a diffusion wave equation. A vector-based river network map which flexibly discretizes river segments was adopted in order to replace the traditional grid-based map which is based on a Cartesian grid coordinate system. The computational efficiency of the proposed flow routing and river network map was tested by executing hydrodynamic simulations with the CaMa-Flood global river model. The simulation results suggest that the computational efficiency can be improved by more than 300% by applying the local inertial equation. It can be improved by a further 60% by implementing the vector-based river network map instead of a grid-based map. It is found that the vector-based map with evenly distributed flow distances between calculation units allows longer time steps compared to the grid-based map because the latter has very short flow distances between calculation units at high latitudes which critically limit time step length. Considering the improvement in simulation speed, the local inertial equation, and a vector-based river network map are preferable in global hydrodynamic simulations with high computational demands such as ensemble or long-term experiments.