Self-excited high frequency combustion instability (HFCI) of first-order tangential (1T) mode was observed in a staged-combustion LOX/Kerosene liquid rocket engine numerically. Two different kinds of 1T patterns, standing wave mode and traveling wave mode, were captured in the present work. In the nominal operation condition, the ratio of oxygen-to-fuel (O/F) was 2.5. Propellant was evenly distributed in all injectors and no HFCI occurred. The chamber pressure obtained from the numerical simulation and experiment showed a good agreement, which validated the numerical model. When the mass flow of fuel for two injectors was modified, severe HFCI occurred. The pressure wave node was located at a fixed diameter, showing a 1T standing wave mode. As the O/F was set 4.4 and the propellant distribution was completely uniform, the numerical result yielded a 1T wave node featured a spinning behavior, which was a traveling 1T wave mode. Once the HFCI arose, no matter what standing mode or spinning mode, the pressure and heat release oscillated totally in phase temporally and coupled spatially. The heat release from combustion was fed into the resonant acoustic mode. This was the thermoacoustic coupling process that maintained the HFCI.