The morphology of neuronal axons has been actively investigated by researchers to understand functionalities of neuronal networks, for example, in developmental neurology. Today's optical microscope and labeling techniques allow us to obtain high-resolution images about axons in three dimensions (3D), however, it remains challenging to segment and reconstruct the 3D morphology of axons. These include differentiating adjacent axons and detecting the axon branches. In this paper we present a method to track axons in 3D by identifying cross-sections of axons on 2D images and connecting the cross-sections over a series of 2D images to reconstruct the 3D morphology. The method can separate adjacent axons and detect the split and merge of axons. The method consists of three steps, modified nonlinear diffusion to remove noise and enhance edges in 2D, morphological operations to detect edges of the cross-sections of axons in 2D, and mean shift to track the cross-sections of axons in 3D. Performance of the method is demonstrated by processing real data acquired by confocal laser scanning microscopy.