The oscillatory behavior of a double-walled carbon nanotubes with a rotating inner tube is investigated using molecular dynamics simulation. In the simulation, one end of the outer tube is assumed to be fixed and the other is free. Without any prepullout of the rotating inner tube, it is interesting to observe that self-excited oscillation can be triggered by nonequilibrium attraction of the ends of two tubes. The oscillation amplitude increases until it reaches its maximum with decrease of the rotating speed of the inner tube. The oscillation of a bitube is sensitive to the gap between two walls. Numerical results also indicate that the zigzag/zigzag commensurate model with a larger gap of >0.335 nm can act as a terahertz oscillator, and the armchair/zigzag incommensurate model plays the role of a high amplitude oscillator with the frequency of 1 GHz. An oblique chiral model with a smaller gap of <0.335 nm is unsuitable for the oscillator because of the steep damping of oscillation.