The removal of noise in image is one of the important issues, and useful as a preprocessing for edge detection, motion estimation and so on. Recently, many studies on the nonlinear digital filter for impulsive noise reduction have been reported. The median filter, the representative of the nonlinear filters, is very effective for removing impulsive noise and preserving sharp edge. In some cases, burst (i.e., successive) impulsive noise is added to image, and this type of noise is difficult to remove by using the median filter. In this paper, we propose an Adaptive Weighted Median (AWM) filter with Decimation (AWM-D filter) for burst noise reduction. This method can also be applied to recover large destructive regions, such as blotch and scratch. The proposed filter is an extension of the Decimated Median (DM) filter, which is useful for reducing successive impulsive noise. The DM filter can split long impulsive noise sequences into short ones, and remove burst noise in spite of the short filter window. Nevertheless, the DM filter also has two disadvantages. One is that the signals without added noise is unnecessary filtered. The other is that the position information in the window is not considered in the weight determinative process, as common in the median type filter. To improve detail-preserving property of the DM filter, we use the noise detection procedure and the AWM-D filter, which can be tuned by Least Mean Absolute (LMA) algorithm. The AWM-D filter preserves details more precisely than the median-type filter, because the AWM-D filter has the weights that can control the filter output. Through some simulations, the higher performance of the proposed filter is shown compared with the simple median, the WM filter, and the DM filter.