We constructed a very accurate fiber bragg grating sensor system using an unbalanced mach-zehnder interferometer which converts the measurand-induced bragg wavelength shift to phase change of th einterference signal. With a shielded reference grating, output phase drift which orginates from the thermal drift on the interferometer was compensated. Mesured accuracy of the constructed system was 0.03 .deg. C and 0.26.mu. strain for temperature and strain measuremtn, respectively. It is over 300 times better resolution compared to the conventional optical spectrum analyzer which has 0.1nm wavelength resolution capability.