Radial force can cause vibration or deformation of workpiece in internal turning process, especially for deep hole turning, which have a negative effect on machining accuracy and surface quality. In this paper, the impact damper theory is investigated and the damped turning cutter is designed. Firstly, the impact damper theory is investigated via modeling and simulation based on Euler–Bernoulli beam theory. Then, the clearance and restitution coefficient are optimized via simulated annealing algorithm with different cutting parameters. The negative real part of the main mode of the damped turning cutter is maximized, which can achieve the stability of cutting process. Finally, the damped turning tool is designed based on impact damper theory and the cutting test is carried out. When n=400r/min, f=0.1mm/r, a_p=0.4 mm, the experimental results show that the vibration acceleration amplitude can be decreased from 46.5m/s² to 4.0m/s² and the roughness can be decreased from 4.62μm to 1.95μm.