A new three-reservoir model was proposed to simulate complex groundwater flow in a karst system where a short-duration pumping test was conducted. The pumping test was conducted in the Houzhai underground river basin located in Puding County, Southwest China. Three sinkholes were used as a pumping and observation well network in the pumping test. Water was pumped from one sinkhole located in the local matrix reservoir. The response of hydraulic head to the pumping was observed at the other two sinkholes located in the conduit network reservoir. Marechal and others (Water Resour Res 44:W05401, 2008) used a two-reservoir model to simulate a long-duration pumping test which provided a good match between the observations and calculations. In this study, a three-reservoir model was developed to represent the local matrix, regional matrix, and conduit network. The regional matrix reservoir was treated as the boundary from which the flow system was recharged. This model can better simulate the site’s hydrogeological conditions. The results show that the observed hydraulic heads agree well with the calculated heads in the conduit network [relative root mean square (rRMS) error = 3.32 %] and in the local matrix (rRMS = 8.43 %). The model also calculated the component volumes of groundwater flow, including the exchange among the three reservoirs. The extent of influence of the pumping test was also characterized in the model. Local matrix storage, recharge from the conduit network, and the recharge from the regional matrix account for about 10.46, 61.28 and 28.26 % of the groundwater pumpage, respectively. The appropriate rate and duration of pumping can be estimated using the calibrated model for the water resources management.