Thermoacoustic instabilities result from the interaction of flow, combustion and sound in combustion systems like industrial burners, gas turbines etc. It is mainly caused when the acoustic field and unsteady heat release are in phase. A prototypical device (laboratory scale) known as Rijke tube is used for studying the phenomena of thermoacoustic instability, in the form of pressure oscillations. The dynamics of the Rijke tube reveals that it has both non- linear and non-normal behavior that triggers the oscillations. State-of-art control techniques (active and passive control laws) have been developed to suppress the thermoacoustic instabilities; however to maintain the system’s performance and stability under various issues like constraints on the control inputs and state vectors, capturing entire non-linear dynamics and disturbances still remains a challenge. Thus, arises a need for developing an advanced controller that addresses the above-mentioned issues. MPC can be used to control thermoacoustic instabilities by reducing high amplitude pressure oscillations effectively with all the constraints, time delays and disturbances. Successive-linearization MPC has unique advantages of utilizing an updated model, concurrent with the changing operating conditions, for active control. It involves simultaneous computation (advantage of the recent advancements in processing hardware) that is exploited for control effort calculations with feedback being received from pressure measurements.