Nowadays, many of the world cities and its peripheral areas are under constant threat of flooding due to high rainfall events. Increased rate of severe flood hazards world-wide have created a demand for understanding the flooding behaviour across various urban and peri-urban catchments. However, simulating the flooding scenarios under limited hydrological data condition is a great challenge for the urban water planners and managers, especially in developing countries. To this, in this study, a combined modelling approach is proposed with the physically based Variable Parameter Muskingum Stage (VPMS) routing model to develop a local rating curve for generating the discharge data from the available stream stage data, which was subsequently used as an input to the Storm Water Management Model (SWMM). The coupled methodology is applied in a typical ungauged urban and peri-urban catchment of eastern India. The proposed SWMM-VPMS model is calibrated for the monsoon (rainy) season of the year 2009, and validated for the monsoon seasons of 2011 and 2014. The performance of the model is satisfactory with the Nash-Sutcliffe efficiency (NSE) estimates of 0.82, 0.89, and 0.89 for the years 2009, 2011, and 2014, respectively. The proposed SWMM-VPMS model can be used for a catchment where the tributary is ungauged while the main river is gauged at a downstream location of the confluence point. This methodology can also be adopted in catchments with missing rating curves. Additionally, the information regarding spatial distribution of channel flow depth at different time can be utilised to have an initial assessment of the flood-vulnerable areas. Keywords: VPMS; SWMM; Urban and peri-urban catchment; Ungauged catchment