Diffusion tensor imaging (DTI) is important for characterizing the structure of white matter fiber bundles as well as detailed tissue properties along these fiber bundles in vivo. There has been extensive interest in the analysis of diffusion properties measured along fiber tracts as a function of age, diagnostic status, and gender, while controlling for other clinical variables. However, the existing methods have several limitations including the independent analysis of diffusion properties, a lack of method for accounting for multiple covariates, and a lack of formal statistical inference, such as estimation theory and hypothesis testing. This paper presents a statistical framework, called VCMTS, to specifically address these limitations. The VCMTS framework consists of four integrated components: a varying coefficient model for characterizing the association between fiber bundle diffusion properties and a set of covariates, the local polynomial kernel method for estimating smoothed multiple diffusion properties along individual fiber bundles, global and local test statistics for testing hypotheses of interest along fiber tracts, and a resampling method for approximating the p-value of the global test statistic. The proposed methodology is applied to characterizing the development of four diffusion properties along the splenium and genu of the corpus callosum tract in a study of neurodevelopment in healthy rhesus monkeys. Significant time effects on the four diffusion properties were found.