Studies of sediment transport problems in mountainous rivers with steep slopes are difficult due to rapid variations in flow regimes, abrupt changes in topography, etc. Sediment transport in mountainous rivers with steep slopes is a complicated subject because bed materials in mountainous rivers are often heterogeneous and contain a wide range of bed material sizes, such as gravel, cobbles, boulders, etc. This paper presents a numerical model that was developed to simulate the river morphology in mountainous rivers where the maximum bed material size is in the range of cobbles. The governing equations were discretized using a finite difference method. In addition, an empirical bed load formula was established to calculate the bed load transport rate. The flow and sediment transport modules were constructed in a decoupled manner. The developed model was tested to simulate the river morphology in an artificial channel and in the Asungjun River section of the mountainous Yangyang Namdae River (South Korea). The simulation results exhibited good agreement with field data.