Carbon nanotubes are applicable to a number of fields such as electron emitter in FED, and high performance composites, etc. They have cylindrical graphitic micro-crystals with nanometer diameters. We purified singlewall carbon nanotubes with nitric acid and removed some of catalysts and amorphous carbon materials. After purification, we broke the carbon nanotubes and made their lengths short with the 3:1 mixture of concentrated sulfuric acid and nitric acid. During purification and cutting, carboxylic acid bond were attached to the open end of singlewall carbon nanotubes (CutSWNTs). Octadecylamine and amino-terminated polystyrene were grafted to CutSWNTs by the condensation reaction of amine and carboxylic acid. Amide bond were characterized with NMR and XPS. CutSWNTs were not dispersed in organic solvents. But, octadecylamine-grafted singlewall carbon nanotubes (ODASWNTs) and polystyrene-grafted singlewall carbon nanotubes (PSSWNTs) were well dispersed in dichloromethane, and aromatic solvents (benzene, toluene, etc). Composites were made by mixing polystyrene with ODASWNTs or PSSWNTs. The composites had higher dynamic storage modulus than polystyrene. They showed an enhanced storage modulus and complex viscosity as well as unusual non-terminal behavior, compared with monodisperse polystyrene matrix. The enhancements of mechanical and rheological properties were caused by good dispersion of carbon nanotubes in polystyrene matrix.