Punctate white matter lesions (PWML) are common in preterm infants. Extensive microstructural changes were observed previously. However, specific changes related to axons and extra-axonal structures remain to be investigated. White matter tract integrity (WMTI) metrics derived from diffusion kurtosis imaging provide information of intra-axonal or extra-axonal spaces. This study aimed to use these metrics to quantify specific variations associated with PWML. Besides reduced fractional anisotropy and increased radial diffusivity, increased diffusivities in extra-axonal and intra-axonal spaces were found. Furthermore, tortuosity and fiber dispersion decreased obviously. These results suggested that PWML would influence axonal reorganization as well as extra-axonal structural integrity.