We demonstrate a largely tunable dispersion fiber Bragg grating (FBG) inscribed in a microstructured polymer optical fiber (mPOF). The bandwidth of the chirped FBG (CFBG) was achieved from 0.11 to 4.86 nm, which corresponds to a tunable dispersion range from 513.6 to 11.15 ps/nm. Furthermore, thermal sensitivity is used to compensate for the wavelength shift due to the applied strain. These results demonstrate that a CFBG in a POF is a promising technology for future optical systems.