Numerical simulations on processes within a hybrid rocket motor were conducted in the past, where most of these simulations carried out majorly focused on steady state analysis. Solid fuel regression rate strongly depends on complicated physicochemical processes and internal fluid dynamic behavior within the rocket motor, which changes with both space and time during its operation, and are therefore more unsteady in characteristics. Numerical simulations on the unsteady operational processes of N2O/HTPB hybrid rocket motor with and without diaphragm are conducted within this research paper. A numerical model is established based on two dimensional axisymmetric unsteady Navier–Stokes equations having turbulence, combustion and coupled gas/solid phase formulations. Discrete phase model is used to simulate injection and vaporization of the liquid oxidizer. A dynamic mesh technique is applied to the non-uniform regression of fuel grain, while results of unsteady flow field, variation of regression rate distribution with time, regression process of burning surface and internal ballistics are all obtained. Due to presence of eddy flow, the diaphragm increases regression rate further downstream. Peak regression rates are observed close to flow reattachment regions, while these peak values decrease gradually, and peak position shift further downstream with time advancement. Motor performance is analyzed accordingly, and it is noticed that the case with diaphragm included results in combustion efficiency and specific impulse efficiency increase of roughly 10%, and ground thrust increase of 17.8%.