Next-generation high-capacity optical networks require flexible allocation of spectrum resources, for which low-cost optical filters with an ultra-wide bandwidth tunability beyond 100 GHz are desired. We demonstrate an integrated band-pass filter with the bandwidth continuously tuned across 670 GHz (117-788 GHz) which, to the best of our knowledge, is the widest tuning span ever demonstrated on a silicon chip. The filter also features simultaneous wavelength tuning and an unlimited free spectral range. We measured an out-of-band contrast of up to 55 dB, low in-band ripples of less than 0.3 dB, and in-band group delay variation of less than 8 ps. This result was achieved using cascaded Bragg-grating-assisted contra-directional couplers and micro-heaters on the 220 nm silicon-on-insulator platform with a very compact footprint of less than 7000 μm2. Another design with the bandwidth continuously tunable from 50 GHz to 1 THz is also presented.