Self-excited combustion instability in an annular combustor with low-swirl flames is studied with a combination of large eddy simulation (LES) and acoustic solvers. Acoustic analysis with a Helmholtz solver provides an estimate of frequencies and modal structures in the annular combustor. LES gives detailed modal dynamics for specific instability modes. Combustion instabilities in the annular combustor including longitudinal, spinning, and standing modes are successfully captured in a single LES. Numerical results show that the instability modes are not constant; they switch among these modes randomly and rapidly. The flow oscillates back and forth in phase with the largest pressure amplitude located near the outlet of the injectors for the longitudinal mode. The azimuthal instability oscillates in the 1A2L mode of the annular system. In the spinning mode, the pressure antinodes move forward while the modal structure keeps constant. For the standing mode, the locations of pressure antinodes are fixed in the annular combustor and the fluctuations at the pressure antinodes keep out of phase. The near-zero value of the mean spin ratio indicates that the dominant azimuthal mode is the standing mode. The azimuthal modes captured by LES are in good agreement with that predicted by Helmholtz solver in terms of frequency and modal structure. The maximum deviation of the predicted frequency is less than 5%. This adds values before the low-swirl injector is placed into the actual annular combustor.