In this paper, we introduce a low computing post processing algorithm to simultaneously suppress blocking and ringing artifacts of compressed video sequences. A new regularization function to incorporate smoothness to neighboring pixels is defined, where the function is composed of four sub-functions combined with pixel-based data fidelity and smoothing terms. Therefore, the solution can be obtained without inverse matrix or vector-matrix computation, so that low complexity implementation is possible. In addition, the regularization parameter controlling the relative importance between the data fidelity and the degree of smoothness is estimated from the available overhead information in decoder, such as, macroblock type and quantization step size. The experimental results show the capability and efficiency of the proposed algorithm.