A novel approach for demodulation of fiber grating sensors with high-resolution is proposed based on a tunable fiber laser interrogating the sensing fiber grating. The fiber laser scanning for interrogation is controlled by computer. The computer synchronously performs data gathering and data processing while it controls laser wavelength scanning. The Bragg wavelength of sensing grating is determined by using the Gaussian-Newton curve fitting approach. The wavelength-shift resolution of this scheme is 0.1 pm, which can be used in the measurement of temperature or strain with high-resolution capability.