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To understand the initiating mechanism of low frequency instability (LFI) in hybrid rocket combustion, numerical calculation was performed using a direct numerical simulation (DNS). Special attention was paid to the effect of the equivalence ratio on the shift in the phase difference between pressure (p’) and heat release oscillations (q’). A change in the equivalence ratio was considered by varying the temperature and composition of the combustion gas that entered into the post combustion chamber. In the obtained results, additional combustion was successfully simulated along with a vortex generation over the backward step, and combustion pressure and heat release oscillations were clearly reproduced as small vortices that move downward. In addition, the obtained results confirmed that the phase difference between pressure and heat release oscillations shifted because of the changes in the propagation speed of the pressure wave when the temperature of the combustion gas changes.