This paper invokes a reactive flow large eddy simulation (LES) framework to simulate combustion instabilities in a sub-scale rocket combustion chamber. A model rocket combustor of Purdue University called the continuously variable resonance combustor (CVRC) [1] is used to simulate and understand the mechanisms of thermo-acoustic instability. The experimental setup allows the length of the oxidizer injector to be varied continuously to excite and sustain longitudinal mode instabilities. This work uses LES for intermediate oxidizer post location, corresponding to combustor acoustic modes maximum power spectrum density. Flamelet generated manifold combustion methodology is employed to capture transient flame dynamics leading to the onset of self-excited and sustained thermo-acoustic instability. Results are presented in the form of peak-to-peak pressure amplitude, and power spectrum density (PSD) compared to test data. The LES appropriately captures pressure fluctuations originating due to coupling of heat release and acoustic waves at the back step location of the combustor and could reproduce the limit cycle behavior with peak-to-peak pressure fluctuations in a close match with the experimental data.