In order to predict local regression rate in swirling-oxidizer-type hybrid rocket chamber, we conduct a loosely coupled computation of flowfield with surface regression of solid fuel in combustion chamber. Three-dimensional Navier-Stokes equations with thermochemical assumption are solved. The local regression rate is determined from considering heat balance on fuel surface. A proper time interval for surface regression in loosely coupled calculation is examined in a test case for simplified chamber model. This method is also applied to solve the flowfield in realistic swirling-oxidizer-type chamber. The computed time-averaged local regression rate along the fuel surface shows a qualitative agreement with the experimental results, whereas the computed regression rate becomes smaller than those for experimental data with similar oxidizer mass flux. Possible causes for this discrepancy are discussed.