Abstract: ‍ ‍Compared with the conventional microwave synthetic aperture radar （SAR）， terahertz SAR have merits in many applications such as video SAR and slow-moving target detection due to the short wavelength. However， there is high-frequency vibration and flight path deviation for the radar platform due to the influence of air flow and the flight characteristics of the platform itself for airborne terahertz SAR， causing the phase error for the echo signal and ghost targets for imaging results. Therefore， the imaging quality of airborne terahertz SAR can be seriously deteriorated by the high-frequency vibration of radar platform. Thus， it is necessary to achieve high-frequency vibration compensation so as to obtain well-focused image. Numerous vibration compensation methods approximate the high-frequency vibration as composition of simple harmonic vibrations at different frequencies. Different from those methods， alternating direction method of multipliers （ADMM） based vibration compensation method without vibration modeling was proposed in this paper to adapt to complex high-frequency vibration. Firstly， the azimuth fast Fourier transform （FFT） was used to obtain the coarsely focused image， and an auxiliary variable was used to construct the objective function which aims to minimize the l₁-norm of the image. Then ADMM was used to solve the optimization problem， and the phase errors updating step was added to each iterative loop according to the principle of minimizing the image entropy. Finally， the phase compensation signal was constructed with the estimate of phase errors and was used to compensate the phase error of the terahertz SAR echo signal. Both simulations of point targets and distributed imaging scene were used to verify the validity of the proposed method. The results of simulations show that the defocus phenomenon can be well suppressed， and the well-focused image can be obtained under the condition of low signal-to-noise ratio.