In the rocket motors background the hybrid rocket engines (HREs) exhibit several advantages over the other two configurations, the liquid rocket engines (LREs) and the solid rocket motors (SRMs). There are also some disadvantages such as the low fuel regression rate and the combustion instability. The purpose of this work is to develop a numerical method capable of observing the combustion instability in the HREs with the aid of the previous studies developed about it. In the experimental tests on the HREs, it was found that the chamber pressure increases from its mean value and it oscillates into a nonlinear limit cycle, the so-called “DC shift“.