A novel aromatic fluorinated tetramine, 2,2-bis[4-(2,4-diaminophenoxy)phenyl]hexafluoropropane (BDAPFP), was successfully synthesized. To maximize the advantages of the linear polyimides and hyperbranched polyimides, a series of novel star-branched fluorinated polyimides BPI-(1–3), which were derived from BDAPFP and anhydride-terminated linear poly(amide acid)s LPAA′-(1–3), were successfully synthesized. For comparison, a series of corresponding linear polyimides LPI-(1–3) were prepared from 4,4′-oxybisbenzenamine (ODA), p-phenylenediamine (PDA) and 3,3′,4,4′-biphenyltetracarboxylic dianhydride (BPDA) with various monomer ratios via the conventional two-step procedure with heating, imidization method. All the polyimides could form strong, flexible and transparent films with an UV-visible absorption cut-off wavelength at 366–398 nm. When compared with the linear polyimide films LPI-(1–3), the star-branched fluorinated polyimide films BPI-(1–3) not only possessed better thermal stability with glass transition temperatures of 283.0–318.0 °C and 5% weight loss temperatures of 544–578 °C and 500–560 °C in nitrogen and air, respectively, but also had improved mechanical properties with tensile strengths of 113–243 MPa, elongation at break of 9.44–9.70% and tensile modulus of 2.09–3.74 GPa. Moreover, the star-branched polyimide films BPI-(1–3) exhibited lower water absorptions of 0.35–0.52%, better dielectric properties with lower dielectric constants of 2.72–3.12 and lower dielectric losses of 0.0028–0.0040 at 1000 kHz.