This paper presents a method to remove blocking artifacts in low bit-rate block-based video coding. The proposed algorithm has two separate filtering modes, which are selected by pixel behavior around the block boundary. In each mode, proper 1D filtering operations are performed across the block boundary along horizontal and vertical directions, respectively. In the first mode corresponding flat regions, a strong filter is applied inside the block as well as on the block boundary, because the flat regions are more sensitive to the human vidual system and the artifacts propagated from the previous frame due to motion compensation are distributed inside the block. In the second mode corresponding to other regions, a sophisticated smoothing filter, which is based on the frequency information around block boundaries, is used to reduce blocking artifacts adaptively without introducing undesired blur. Even though the proposed deblocking filter is quite simple, it improves both subjective and objective image quality for various image features.