Abstract Reconstructing neuron morphology is central to uncovering the complexity of the nervous system. That is because the morphology of a neuron essentially provides the physical constraints to its intrinsic electrophysiological properties and its connectivity. Recent advances in imaging technologies generated large quantities of high-resolution 3D images of neurons in the brain. Furthermore, the multispectral labeling technology, Brainbow permits unambiguous differentiation of neighboring neurons in a densely labeled brain, therefore enables for the first time the possibility of studying the connectivity between many neurons from a light microscopy image. However, lack of reliable automated neuron morphology reconstruction makes data analysis the bottleneck of extracting rich informatics in neuroscience. Supervoxel-based neuron segmentation methods have been proposed to solve this problem, however, the use of previous approaches has been impeded by the large numbers of errors which arise in the final segmentation. In this paper, we present a novel unsupervised approach to trace neurons from multispectral Brainbow images, which prevents segmentation errors and tracing continuity errors using two innovations. First, we formulate a Gaussian mixture model-based clustering strategy to improve the separation of segmented color channels that provides accurate skeletonization results for the following steps. Next, a skeleton graph approach is proposed to allow the identification and correction of discontinuities in the neuron tree topology. We find that these innovations allow our approach to outperform current state-of-the-art approaches, which results in more accurate neuron tracing as a tree representation close to human expert annotation.