The structure and thermal expansion of multi-walled carbon nanotubes (MWNTs) with different diameters, prepared through the catalytic decomposition of vaporized benzene, were studied by x-ray diffraction at different temperatures, combined with scanning electron microscopy, transmission electron microscopy and electron diffraction. In comparison with that of the as-grown MWNTs, decreasing d002 and increasing Lc of MWNTs after high temperature treatment (HTT) were obvious. However, the smaller the diameter of MWNTs, the more difficult the graphitization. The structural strain εc representing the distribution of interlayer spacing increased with increasing nanotube diameter. Considering the observations of asymmetrical lattice fringe for small MWNTs and polygonization morphology for big MWNTs after HTT, the crystallite size Lc and the radial thermal expansion αc of MWNTs with different diameters were comparatively analysed in view of the energy. Presumably 50 nm may be the critical diameter for polygonization of MWNTs. Based on these facts, the mechanism of the graphitization process for MWNTs was discussed and the structure models of the MWNTs before and after HTT were suggested.