A large torque large stroke rotary actuator with hybrid drive of a piezoelectric stack and a motor, and a method are disclosed. The actuator comprises an actuator piezoelectric stack; a rhombic ring installed at an outer side of the piezoelectric stack; a threaded rod connected to an end of the rhombic ring; a lock-up nut which is connected with the threaded rod through a thread, meanwhile acts as a rotating mechanism rotor, and is embedded with a drive rotor at an outer side; a connecting rod with a large pitch lead screw and connected to the other end of the rhombic ring, a lock-up nut connected with the connecting rod through a thread, used as a rotor and embedded with a drive stator at an outer side; a screw nut connected with the threaded connecting rod at the other end through the large pitch screw; and thrust ball bearings installed to two ends of the screw nut, the above structure being packaged in a housing. The invention further provides an actuation method, and can achieve stepping output of large torque large stroke rotary motion by driving the piezoelectric stack and the motor according to a certain order; and the actuator has the characteristics of large rotation drive stroke, bidirectional output large torque, power outage lock-up, and reliable and stable locking.