We present a rapid algorithm for identifying the current-carrying backbone in the percolation model. It applies to general two-dimensional graphs with open boundary conditions. Complemented by the modified Hoshen-Kopelman cluster labeling algorithm, our algorithm identifies dangling parts using their local properties. For planar graphs, it finds the backbone almost four times as fast as Tarjan's depth-first-search algorithm, and uses the memory of the same size as the modified Hoshen-Kopelman algorithm. Comparison with other algorithms for backbone identification is addressed.