Connected component labeling is a frequently used image processing task in many applications. Moreover, in recent years, the use of 3D image data has become widespread, for instance, in 3D X-ray computed tomography and magnetic resonance imaging. However, because ordinary labeling algorithms use a large amount of memory and 3D images are generally large, labeling 3D image data can cause memory shortages. Furthermore, labeling a large image is time-consuming. In this paper, we proposed new memory-efficient connected component labeling algorithm for 3D images with parallel computing. In this method, we accelerate the labeling process using parallel computing. In addition, we use a spans matrix and compressed label matrix to reduce memory usage. We also use an equivalence chain approach to speed up the calculation. Furthermore, the algorithm has two options for further processing performance or further memory savings. In the experiments on real examples, the proposed algorithm with the option for processing speed was faster and used less memory than the conventional label equivalence method. In contrast, with the proposed method using the memory-efficient option, we could further reduce memory from one-eighth to one-thirteenth that used by the label equivalence method while maintaining the same performance.