The objective of the present study is to understand the effects of added hydrogen and operating conditions on turbulent fluctuation and dynamic flame stability in a turbulent diffusion flame with methane/hydrogen hybrid fuel. A large eddy simulation (LES) technique is used to predict turbulent statistics accurately. A parametric study is performed by changing hydrogen concentration, background pressure and temperature, which include the conditions similar as in a direct injection internal combustion (IC) engine. Turbulent statistics such as EMS flow fields, flame stability index and combustion noise are analyzed to evaluate the flame stability. A normalized Rayleigh index proves to be a useful indicator for the stability of turbulent diffusion flame, as compared to the RMS of flow variables. From the combustion noise spectra, hydrogen addition stabilizes mainly the primary vortex shedding in the standard condition but reduces the noise level in the entire frequency range as the compression ratio increases. Also, it is concluded that stabilization of unsteady fluctuation is highly correlated to the reduced flame length. Copyright (C) 2015, Hydrogen Energy Publications, LLC. Published by Elsevier Ltd. All rights reserved.