The ADMM (alternating direction method of multipliers) with appropriate parameters plays a successful role in solving linear inverse problems (including image restoration). But the results obtained by ADMM are sensitive to the choices of the penalty parameter, and this bad robustness brought some troubles in its applications. Based on a scheme of choosing the penalty parameter adaptively, a RADMM (robust ADMM) was proposed to tackle this shortcoming. Through analyzing optimization conditions and convergence of RADMM, we can conclude that the adaptive control of the penalty parameter provides good robustness, faster speed of convergence and better solution. And the experiments show that, in the application of image restoration based on the Parseval tight frame, the RADMM is robust to the choices of the penalty parameter, outperforms the ADMM, and is far superior to other alternative state-of-the-art methods.