Thermoacoustic instabilities are commonly encountered in the development of aeroengines and rocket motors. Research on the fundamental mechanism of thermoacoustic instabilities is beneficial for the optimal design of these engine systems. In the present study, a thermoacoustic instability model based on the lean premixed gas turbines (LPGT) combustion system was established. The longitudinal distribution of heat release caused by the intrinsic instability of flame front was considered in the model. Effects of different heat release distributions and characteristic parameters (Lewis number Le, Zeldovich Number , and Prandtl number Pr) of the premixed gas on thermoacoustic instability behaviors of the LPGT system were investigated based on the established model. Results show that the LPGT system features have two kinds of unstable thermoacoustic modes. The first one corresponds to the natural acoustic mode of the plenum and the second one corresponds to that of the combustion chamber. The characteristic parameters of the premixed gases have a large impact on the stability of the system and can even change the system from stable to unstable state.