In this work, multi-walled carbon nanotubes (MWCNTs) were functionalized with azide-terminated polystyrene (PS). The functionalized MWCNTs were mixed with styrene-b-(ethylene-co-butylene)-b-styrene (SEBS), a triblock copolymer, to produce electrical conductive nanocomposites. SEBS block copolymers consist of polystyrene (PS) hard domains and ethylene and butylene soft segments. Therefore, the combination of the MWCNTs and SEBS in a well-mixed nanocomposite with stable morphology may lead to a material with new and interesting properties for electronic devices. The PS for the functionalization with designed molecular weight (Mn) and narrow molecular weight distribution (Mw/Mn) was synthesized by atom transfer radical polymerization (ATRP) of styrene followed by end group transformation from bromide to azide and then reaction with the MWCNTs. Mn~2500g/mol and Mw/Mn~1.1 were measured by gel permeation chromatography (GPC) The functionalization was confirmed by infrared spectroscopy (IR) and thermogravimetric analyses (TGA). To produce the nanocomposites the functionalized MWCNTs were mixed with SEBS using tetrahydroxyfuran (THF) as a solvent and then precipitated in methanol, a non-solvent. Films of these nanocomposites were produced by melt-pressing. The macroscopic dispersion of the MWCNTs through the polymer matrix was analyzed by optical microscopy. The electrical AC conductivity of the nanocomposites was measured by impedance method. The results showed that films containing 0.1 and 0.5 % (v/v) of PS-functionalized MWCNTs exhibited significantly improved electrical conductivity compared to SEBS films containing pristine MWCNTs. Optical micrographs showed a better dispersion of the functionalized MWCNTs compared with the pristine MWCNTs.