Abstract Focusing on the collaborative fuel supply and acceleration problem of multi combustor turbine engine, a variable geometry composite regulation acceleration control law design method based on the combination of compressor intermediate stage air bleed(CIB) and low-pressure turbine guide vanes(LTGV) is proposed. The multi combustor collaborative fuel supply law and variable geometry regulation law during acceleration process are obtained by Particle Swarm Optimization-Sequence Quadratic Program (PSO-SQP) optimization, and the composite regulation acceleration control strategy of dual/single combustion chamber idle acceleration process is explored. The multi combustor acceleration process simulation results indicate that the variable geometry composite regulation method can effectively alleviate the stability margin limitation of the compressor during the initial acceleration stage. Compared with conventional acceleration methods, the maximum relative reduction in acceleration time of our method reaches 26%; Enhancing the combustion exergy efficiency during the acceleration process can significantly improve the engine's acceleration performance.; For the acceleration process from single combustion chamber idle operation to normal operation of a dual combustion chamber, simultaneous fuel supply from both combustion chambers during acceleration has a shorter acceleration time. The research results of this paper can provide important references for the design of transition state control systems for multi combustor turbine engines.