Recently, the video images are introduced in the measurement and the monitoring system. The image sequences, which are obtained by these systems, are corrupted by additive noise. The restoration of the image sequences corrupted by additive noise is important to obtain the high quality image and the high compression. In this paper, we propose a restoration method for the image sequences corrupted by Gaussian noise. The conventional restoration methods are archived by spatio-temporal filtering after the motion estimation. The accuracy of the motion estimation of the conventional method is affected by the Gaussian noise. Therefore, the filtering performance after the motion estimation is not satisfied. In this paper, to overcome this defect without increasing the calculation time, we propose a spatio-temporal separable data-dependent weighted average filter with the motion estimation. The first process of the proposed method, we use the spatial filter for the corrupted image sequences. This process regards as the pre-filtering for motion estimation and realizes the robust motion estimation. The second process is the motion estimation process. Since the motion is estimated using the output of the first process, the accuracy of estimation is high. In the third process, the temporal filter is used to reduce the noise with the motion compensation. We demonstrate the performance of the proposed method through a lot of simulation results.