The invention aims to provide a bypass afterburning composite regenerative turbo supercharging system of a boiler. The system comprises a boiler, a gas compressor, a turbine, valves, a bypass pipe, an afterburning chamber, a gas storage tank, a regenerator and a mixing pipe, wherein an inlet of the gas compressor is provided with the mixing pipe, and an outlet of the gas compressor is connected with the boiler through a regenerative pipe; a first adjusting valve is arranged between the mixing pipe and the regenerator; a first branch of an outlet of the turbine is connected with atmosphere; a second branch of the turbine is connected with the regenerator through a second adjusting valve; the bypass pipe, a bypass valve, the afterburning chamber and a check valve are arranged between the gas compressor and the turbine; and the gas storage tank is connected with the afterburning chamber through a gas escape valve. Through the system, the running of a supercharging set is free from limitation of a flue gas and air system and a steam system of the boiler, transient response characteristic of a supercharged boiler is improved, low working condition performance and starting performance of the supercharged boiler are improved, thermal balance and steam balance of a ship power device are more stable, and viability of a ship is improved.