We investigated the dependences of Brillouin frequency shift (BFS) on strain and temperature in a perfluorinated graded-index polymer optical fiber (PFGI-POF) at 1.55 μm wavelength. They showed negative dependences with coefficients of -121.8 MHz/% and -4.09 MHz/K, respectively, which are -0.2 and -3.5 times as large as those in silica fibers. These unique BFS dependences indicate that the Brillouin scattering in PFGI-POFs has a big potential for strain-insensitive high-accuracy temperature sensing.