To study the combustion stability of liquid rocket engines with hypergolic propellant more comprehensively, external pressure pulse excitation was applied to the UDMH (unsymmetrical dimethylhydrazine)/NTO (methylhydrazine) pre-combustor. The effects of pressure pulse intensity, spray characteristics (droplet diameter and spray cone angle), and combustion mechanism on combustion stability characteristic frequencies and attenuation characteristics after excitation were investigated. The simulation results show that all operation conditions capture the first three longitudinal frequencies of the pre-combustor, and all factors have a greater impact on frequencies with higher orders. Increasing the pulse intensity and reducing the droplet diameter are not conducive to combustion stability. The influence of the spray cone angle on the combustion stability is not monotonous. The pre-combustor has good stability when the spray cone angle is 70°. Different combustion mechanisms have a significant effect on the results before and after pressure pulses, and considering a more complete combustion process may increase the attenuation time in the pre-combustor. The obtained rules can provide a reference for the design and simulation of hypergolic liquid rocket engines, which is beneficial for predicting and evaluating the combustion stability of liquid rocket engines.