.[.A method and apparatus to remove a block effect and a ring effect appearing in a compression-coded image is disclosed. The present invention is especially applicable to an image compression-coded at a low bit rate. In particular, the present invention includes a variety of masks for the removal of the block/ring effect. Thus, one mask is select for a pixel to be filtered. Moreover, candidate pixels to be averaged with the pixel to be filtered is selected from the pixels of the selected mask to better maintain the details of the image, and a weight is applied to improve the calculation speed of the averaging operation. More particularly, the masks according to the present invention have longer tabs toward adjacent blocks at boundaries of the given block to remove the block and ring effect..]. .Iadd.In the method, a filtering mask is selected based on a position of a pixel to be filtered. The filtering mask includes the pixel to be filtered and at least one candidate pixel. The pixel to be filtered is filtered by applying a weighted averaging operation to the pixel to be filtered and the at least one candidate pixel. The weighted averaging operation includes applying weight to at least one of the pixel to be filtered and the at least one candidate pixel in producing a weighted sum value, and performing a shift operation on the weighted sum value to divide by a desired value..Iaddend.