Digital reconstruction of neurons from microscope images is an important and challenging problem in neuroscience. In this paper, we propose a model-based method to tackle this problem. We first formulate a model structure, then develop an algorithm for computing it by carefully taking into account morphological characteristics of neurons, as well as the image properties under typical imaging protocols. The method has been tested on the data sets used in the DIADEM competition and produced promising results for four out of the five data sets.