A kind of compact near infrared spectrometer based on fiber Fabry-Perot (FFP) Filters is proposed in this paper. In order to reduce the nonlinearity and hysteresis effects of FFP and realize wavelength measurement accurately, a group of fiber Bragg gratings(FBGs) with fixed center wavelength are employed as a wavelength reference. Particle swarm optimization (PSO) algorithm is employed in finding the peak positions of FBGs accurately. On the base of that, polynomial fit is employed to model wavelength-voltage relationship of FFP online in each scanning cycle. Hence a kind of a compact near infrared spectrometer has been designed. Experiments have demonstrated the accuracy of wavelength measurement of the system. The range of the wavelength of the proposed spectrometer is 1490～1590 nm, the maximum absolute wavelength measurement error is as low as 0.03 nm and the spectra resolution is up to 0.4 nm.