Nanocomposites of polyimides (PI) with covalently grafted polyhedral oligomeric silsesquioxane (R7R′Si8O12 or POSS) units were prepared by thermally‐initiated free‐radical graft polymerization of methacrylcyclopentyl‐POSS (MA‐POSS) with the ozone‐pretreated poly[N,N′‐(1,4‐phenylene)‐3,3′,4,4′‐benzophenonetetra‐carboxylic amic acid] (PAA), followed by thermal imidization. The chemical composition and structure of the PI with grafted methacrylcyclopentyl‐POSS side chains (PI‐g‐PMA‐POSS copolymers) were characterized by nuclear magnetic resonance (NMR), X‐ray diffraction (XRD), and thermogravimetric analysis (TGA). The POSS molecules in each grafted PMA side chain of the amorphous PI films retained the nanoporous crystalline structure, and formed an aggregate of crystallites. The PI‐g‐PMA‐POSS nanocomposite films had both lower and tunable dielectric constants, in comparison with that of the pristine PI films. Dielectric constants (κ's) of about 3.0–2.2 were obtained. The present approach offers a convenient way for preparing low‐κ materials based on existing PI's. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci, 2006