Nanocomposites of poly(4-methyl-1-pentene) (PMP) with various weight fractions of multiwall carbon nanotubes (MWNT's) were prepared by melt compounding. The nanocomposites are characterized for structure using scanning electron microscopy. The viscoelastic behavior of the nanocomposites is investigated in solid as well as melt state. The study reveals a significant increase in storage modulus especially in the rubbery regime of the polymer matrix and reduced tan delta. Rheological properties in melt show that the complex viscosity and shear storage modulus are increased as a result of incorporation of MWNT. A systematic decrease in the cross over frequency is noted which is attributed to the increased relaxation time. In dielectric analysis, composition dependent enhanced permittivity and conductivity are observed. The thermal stability of the polymer is found to be significantly improved in presence of MWNT's.