For the problem of image restoration of observed images corrupted by impulse noise, the widely used TVL1 model may deviate from both the data acquisition model and prior model, especially for high noise levels. To overcome this problem, based on MCP function, a new model called TV-MCP and its approximation method were proposed. It is proved that the approximation method converges globally to a stationary point of TV-MCP model. Alternating direction method of multipliers was applied to solve the approximation sub-problem. In the numerical experiments, TVL1 and TV-MCP were applied to the problem of image de-noising and de-blurring in the presence of impulse noise, which verifies the effectiveness of the proposed model and method. The results show that TV-MCP outperforms TVL1, especially for the high noise level image de-noising. The maximum SNR value of TV-MCP image restoration can reach 2 times that of TVL1 method.