The invention provides a pressure relief type anti-swing control device used in the rotation positioning and braking process of engineering machines. The pressure relief type anti-swing control device comprises a pressure oil source, a rotation control valve, a pressure relief control valve, a hydraulic motor, an oil pressure detection module and a controller module. The pressure oil source is connected with the rotation control valve. The rotation control valve is connected with the hydraulic motor. The pressure relief control valve is also connected with the hydraulic motor. The oil pressure detection module is connected with two working oil cavities of the hydraulic motor and used for detecting the oil pressure change condition. The controller module makes the first working oil cavity or the second working oil cavity of the hydraulic motor communicate with or cut off from an oil tank by switching the working state of the pressure relief control valve according to oil pressure change information of the working oil cavities of the hydraulic motor. According to the technical scheme, the reverse backswing phenomenon happening in the rotation positioning and braking process of the engineering machines can be effectively restrained. Meanwhile, the invention provides a pressure relief type anti-swing control method including the pressure relief type anti-swing control device used in the rotation positioning and braking process of the engineering machines.