This paper reports a digital demodulation scheme for interrogating fiber Bragg grating (FBG) sensors based on a real-time calibration technique. The system controls a tunable fiber Fabry-Perot filter (TFFP) with sawtooth wave voltage and synchronous signal of its digital phase to interrogate FBG sensors in a single fiber. Meantime, a reference FBG and a digital thermometer provide an accurate reference wavelength, which is used to calibrate the wavelength readout of the TFFP in real-time by a digital signal processor (DSP). This method eliminates the measurement error induced by temperature drift, nonlinearity and creepage of TFFP. The result demonstrates that this experimental system has scanning range of 1520～1570 nm, scanning frequency of 100 Hz, measured wavelength resolution of 5 pm, and measured strain resolution of 4.13 με.