The dragging teaching method is easy to operate and has high teaching efficiency, which is more in line with modern flexible production. To realize the dragging teaching of industrial robots, it is necessary to accurately measure the external force and control the motion caused by the external force. In order to measure the external force exerted by the operator without torque sensor, an external force observer based on disturbance Kalman filter was designed. The observer takes the external joint torque as the disturbance term, and introduces generalized momentum to establish the state space equation of the robot system, and then uses the Kalman filter algorithm to obtain the optimal observed value of the external torque. Among them, in order to improve the estimation accuracy, the robot dynamic model was established by combining the rigid-body dynamic model and a deep neural network, which not only avoids modeling the complex friction torque but also compensates for the unmodeled factors through the deep neural network. Besides, in order to realize the leading control of the robot in the process of dragging teaching, the dynamic response relationship between the teaching motion and the external torque is equivalent to a mass damping system. An admittance control method with adaptive damping was proposed to convert the observed external torque into the desired joint angle of the teaching motion, and adaptively adjust the system damping parameters according to the change trend of the external torque to improve the teaching effect of the robot. The experiment results show that the proposed dynamic model has a lower mean square root error in the prediction torque, which can reduce the error by no less than 20%. The proposed control scheme can realize the dragging teaching without torque sensors on the six-degree-of-freedom industrial robot, and the adaptive damping method can reduce the torque required to rotate the joint by about 19%, which is more conducive to the start and stop of the teaching motion.