Simulation of flood inundation at metric resolution is important for making hazard information useful to a wide range of end-users involved in flood risk management, and addressing the alarming increase in flood losses that have been observed over recent decades. However, high data volumes and computational demands make this challenging over large spatial extents comparable to the metropolitan areas of major cities where flood impacts are concentrated, especially for time-sensitive applications such as forecasting and repetitive simulation for uncertainty assessment. Additionally, several factors present difficulties for numerical solvers including combinations of steep and flat topography that promote transcritical flows, the need to resolve flow in relatively narrow features such as drainage channels and roadways in urban areas which channel flood water during extreme events, and the need to depict compound hazards resulting from the interaction of pluvial, fluvial and coastal flooding. A new flood inundation model is presented here to address these challenges. The Parallel Raster Inundation Model (PRIMo) solves the shallow-water equations on an upscaled grid that is far coarser than the underlying raster digital topographic model (DTM), and uses a subgrid modeling approach so that the solution benefits from DTM-scale topographic data. Additionally, an approximate Riemann solver is applied in an innovative way to integrate fluxes between cells, as needed to update the solution by the finite volume method, which makes the method applicable to subcritical, supercritical and transcritical flows. PRIMo is implemented using a two-dimensional domain decomposition approach to Single Process Multiple Data (SPMD) parallel computing, and overlapping communications and computations are implemented to yield ideal parallel scaling for well-balanced test cases. With both a subgrid model and ideal parallel scaling, the model can scale to meet the demands of any application. Several benchmarks are presented to demonstrate predictive skill and the potential for timely, whole-city, metric-resolution flooding simulations. Limitations of the methods and opportunities for improvements are also presented.