Connected-component labeling is an important process in image analysis and pattern recognition. It aims to deduct the connected components by giving a unique label value for each individual component. Many algorithms have been proposed, but they still face several problems such as slow execution time, falling in the pipeline, requiring a huge amount of memory with high resolution, being noisy, and giving irregular images. In this work, a fast and memory-efficient connected-component labeling algorithm for binary images is proposed. The proposed algorithm is based on a new run-base tracing method with a new resolving process to find the final equivalent label values. A set of experiments were conducted on different types of binary images. The proposed algorithm showed high performance compared to the other algorithms.