A distributed optical fiber grating wavelength interrogator based on fiber Fabry Perot tunable filter(FFP-TF) was proposed, which could measure dynamic strain or vibration of multi-sensing fiber gratings in one optical fiber by time division way. The wavelength demodulated mathematical model was built, the formulas of system output voltage and sensitivity were deduced and the method of finding static operating point was determined. The wavelength drifting characteristic of FFP-TF was discussed when the center wavelength of FFP-TF was set on the static operating point. A wavelength locking method was proposed by introducing a high-frequency driving voltage signal. A demodulated system was established based on Labview and its demodulated wavelength dynamic range is 290pm in theory. In experiment, by digital filtering applied to the system output data, 100Hz and 250Hz vibration signals were measured. The experiment results proved the feasibility of the demodulated method.