The invention provides a sequential turbocharging system anti-surge control device and a control method. The sequential turbocharging system anti-surge control device is composed of a diesel engine speed transducer, a turbo-charger speed transducer, a pressure pickup, an air flowmeter, an air valve, a gas valve, an air circulating valve, an air bypass valve, an air circulating pipeline, an air bypass pipeline, a signal conditioning module, a signal acquiring module, a signal processing module, a storing module, an electromagnetic module and a valve driving device. The method is as follows: acquiring signals of each sensor by a control device; judging whether the interval time of the opening of the gas valve and the air valve is in the allowable range; comparing the detected operation point information with a set control line to obtain whether a surge indication exists or not, and giving corresponding instruction to regulate the air circulating valve and the air bypass valve. The invention can greatly reduce surge events taking place in the process of diesel engine sequential turbocharging system conversion, prolonging the service lift of the turbo-charger and improving transient performance of the diesel engine sequential turbocharging system in conversion process.