A novel tunable photonic microwave filter based on reconstruction equivalent chirp (REC) superstructure fiber Bragg grating (SFBG) is proposed. SFBGs with different slope of group time delay can be neatly designed and fabricated using a uniform phase mask according to the REC technology. As basic time delay among taps of FIR filter, the differential group delay among SFBGs determine the free spectral range (FSR) of the filter. Thus a tunable FSR can be realized by tuning the wavelength of the tunable laser source (TLS) which determine the time-delay difference. The simulation result shows that the FSR can be continuously tuned from 21 GHz to 33 GHz. In fact, this novel tunable filter can be realized in terms of any given frequency band and tuning range in theory due to the flexibility of the REC technology.