The purpose of this study is to develop a computational method to predict fuel regressions for hybrid rocket solid fuels. The shape of the flow field changes depending on the regression and vaporization of the solid fuel. This shape change and the heat flux from the combustion gas to the fuel are mutually dependent. Therefore a computational method that can accurately predicts both of the fuel regression and the heat flux is necessary to clarify the mutual dependence of them. In this study, we have developed a computational method to predict the regression phenomenon including the effect of the shape change of the flow field. The developed code predicts the regression phenomena by repeating gas-phase calculations and regression-phase calculations. The wall consisting of grids permits the flow field to be an arbitrary shape. As the first step, the complex chemical reaction was not included and numerical results were compared with a sublimation phenomenon of naphthalene in a non-combustion flow. Numerical results successfully predicted Nusselt number change due to regression qualitatively.