The invention discloses a spherical rescue robot with a rolling-jumping function and a control method, belongs to the technical field of rescue robots, and relates to a spherical robot which is used for disaster search and rescue and has rolling and jumping functions and a control method. The robot is composed of a left hemispheroid, a right hemispheroid, a center control bin and a plurality of identical magneto-rheological thrust mechanisms. Each magneto-rheological thrust mechanism is composed of a reset spring, a thrust mechanism shell, a magneto-rheological material, an electromagnetic coil, a connecting bolt, a nut, a magneto-rheological material-water diaphragm, water, a sealing ring and a ground supporting rod. According to the control method, the center control bin is used for controlling, the IMU sensor measures the current pose and acceleration data of the spherical robot, the power-on state and the power-on time of each electromagnetic coil are controlled, the internal ground supporting rods are controlled to pop out to impact the ground, and power is provided for the spherical robot. The spherical robot is compact in structure, high in environment adaptability and low in movement energy consumption, and the problem of multi-group collaborative rolling-jumping driving in a small-size space of the spherical robot is effectively solved.