The prediction of peak flow and the simulation of flood hydrographs in a stream or river is a very complex process. An application of a spatially distributed hydrologic model WetSpa working on a daily time scale is presented in this paper. The model combines elevation, soil and landuse data within a GIS framework, and predicts flood hydrograph and the spatial distribution of hydrologic characteristics through a watershed. The hydrological processes considered in the model are precipitation, interception, depression, surface runoff, infiltration, evapotranspiration, percolation, interflow, groundwater flow, and water balance in the root zone and the saturated zone. This version of the WetSpa model uses a modified rational method to calculate runoff and an energy balance approach to estimate the snowmelt runoff based on temperature data. The main focus of the paper is on discussing the simulation of a flood hydrograph as consequence of rainfall and snowmelt. The watershed is represented as a grid cell mesh, and routing of runoff from each cell to the basin outlet is accomplished using the first passage time response function based on the mean and variance of the flow time distribution, which is derived from the advection-dispersion transport equation. The model is applied to the Hornad river basin located in Slovakia. Daily hydrometeorological data from 1993 to 2000, including precipitation, temperature, evaporation, and windspeed, are used as input data to the model. For the simulation of hydrographs at the basin outlet and at the flow monitoring stations inside the catchment, the basin was divided into 223 subcatchments, corresponding to the threshold value of 1000 cells when delineating the stream network based on topographic flow accumulation. The calibration process is mainly performed for the global model parameters, whereas the spatial model parameters are kept as default values. The initial global model parameters are specifically chosen according to the basin characteristics as discussed in the documentation and user manual of the model. Results of the simulations show a good agreement between calculated and measured hydrographs at the outlet of the basin (Nash-Sutcliffe efficiency is equal to 74%). An interesting period, with snow accumulation followed by snowmelt producing a flood is discussed in detail.