Single-walled carbon nanotubes (SWNTs) with a narrow diameter distribution are synthesized by thermal chemical vapor deposition (CVD) of methane over Fe/MgO catalyst on the basis of parametric study considering Fe loading, reaction temperature and time, methane concentration, and structure of a support material. We found that the porous MgO support gives the SWNTs with a narrow diameter distribution with the mean diameter and standard deviation of 0.93 and 0.06 nm, respectively, only when the Fe loading and reaction temperature are relatively low. The higher Fe loading and/or the higher reaction temperature enlarged the nanotube diameter, forming double-walled carbon nanotubes (DWNTs) in addition to SWNTs. This result indicates that only the diameter of Fe nanoparticles determines the growth of either SWNTs or DWNTs on the MgO support. The fluorescence and absorption spectra of the nanotube dispersion in D2O solution with sodium dodecyl sulfate (SDS) were studied to identify their chirality distribution. The fluorescence of the uniform-diameter SWNTs indicates the formation of the near armchair structures. On the other hand, the SWNTs synthesized over the catalyst with a high Fe loading, 3 wt %, showed a wide chirality distribution including the near zigzag structure. The synthesis of the SWNTs with a narrow diameter distribution could be applied to the selection of SWNTs with a specific chirality based on postsynthesis separation.