In this study, the effect of changes in the port diameter, length, and activation energy of solid fuel on rocket performance was investigated to propose the design points of the solid fuel for hybrid rockets based on hydrogen peroxide and high-density polyethylene propellants. Moreover, a numerical estimation code was developed based on the regression rate equation derived from the experiments, and the developed code was assessed for the effectiveness of the multiport solid fuel design and the scale effect by comparing the estimation and experimental results. Based on the parametric study of the solid fuel and numerical estimation code, a hybrid propulsion system with different scales was designed, and design modification for the multiport solid fuel of the 1000-N class hybrid rocket applied to a Woorisae-II sounding rocket was also performed. Small sounding rockets of different scales were designed by integrating the hybrid propulsion system, recovery system with spring control, and rocket avionics. Based on the performance data derived through numerical estimation, a six-degree-of-freedom trajectory simulation was performed to predict the altitude reached by the rocket.