Finding k-edge connected components (k-ECCs) is widely used to investigate the major cohesive structures within a graph. Traditional methods utilizing global minimum cut to split the graph iteratively are too slow to deal with graphs of a large size. Recently, approximate algorithms based on a decomposition framework have been proposed to speed up the process. However, these algorithms produce low-quality results in graphs containing vertex pairs that are k-connected but do not belong to a k-ECC. In this paper, we propose a decomposition framework that utilizes a local edge connectivity check method to obtain high-quality results in a shorter period. The proposed method utilizes an improved maximum flow algorithm to detect k-ECCs from local k-cores by merging more vertices in each iteration than existing methods. Moreover, a pruning strategy is applied in the decomposition framework to reduce unnecessary branches in the decomposition tree. Our experimental results on both synthetic and real graphs show that our proposed algorithm is faster than the state-of-the-art algorithms in most datasets and achieves effective results among the approximate algorithms with a 96% accuracy on our experimental datasets. •An efficient local edge connectivity check based decomposition framework to detect k-ECCs with high accuracy of results.•A k-core based maximal merging and a pruning strategy for optimizing the algorithm processing time and the height of decomposition tree.•An improved augmenting path flow method to directly calculate the minimum cut of two vertices in the check procedure.•Experimental results show that the algorithm can detect k-ECCs with outstanding speed while producing high-quality results (96% accuracy).