One main physical feature of hybrid rocket combustion is its diffusion flame nature that has required excessively long combustion chamber which leads to undesirable large slenderness of a rocket configuration. The diffusion flame also results in generally low combustion efficiency of hybrid rockets. Some remedial designs have used liquefying solid grain, such as paraffin, or mixing enhancement mechanisms to boost the overall fuel regression rate and combustion efficiency. Thus, shortened combustion chambers can be used to deliver reasonable thrust performance of hybrid rockets. In the present study, a compact hybrid rocket motor design is investigated to provide a form factor with small slenderness, which is suitable for improving the overall system designs for hybrid rockets. This design concept features in multiple vortical flow structures such that much enhanced combustion efficiency can be obtained. A 3-D computational model with finite-rate chemistry using reduced kinetics mechanism and radiative heat transfer effects are employed in the present investigation to assess the mixing effectiveness and combustion efficiency of the present design. This computational model has been validated for a wide range of rocket propulsion design problems, including single-port hybrid rocket motors with mixing enhancement vortex generator devices. The internal ballistics and flame structure in the present multiple vortical-flow hybrid rocket engine designs using HTPB fuel with nitrous oxide or hydrogen peroxide oxidizers are investigated.