The recent explosive growth of multimedia data has posed a new set of challenges in computer vision, and video summarization (VS) techniques are increasingly important to automatically summarize a large amount of multimedia data in an effective and efficient manner. Recent years have witnessed the rise and developments of sparse representation based approaches for VS. While the existing methods select keyframes according to the information contained in the single frame, and such a selection based solely on single-frame information may not be robust. Therefore, in this paper, the information of the single frame's neighborhood is taken into consideration, and different weights are assigned to these neighbouring frames. We formulate the VS problem as a weighted neighborhood based representation model, and design a greedy pursuit algorithm to extract keyframes. Experimental results on a benchmark dataset demonstrate that the proposed method can outperform the state of the arts.