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Strain engineering has been demonstrated to be an effective knob to tune the bandgap in perovskite oxides, which is highly desired for applications in optics, optoelectronics, and ferroelectric photovoltaics. Multiferroic BiFeO3 exhibits great potential in photovoltaic applications and its bandgap engineering is of great interest. However, the mechanism of strain induced bandgap engineering in BiFeO3 remains elusive to date. Here, we perform in situ ellipsometry measurements to investigate the bandgap evolution as a function of uniaxial strain on freestanding BiFeO3 films. Exotic anisotropic bandgap engineering has been observed, where the bandgap increases (decreases) by applying uniaxial tensile strain along the pseudocubic [100]p ([110]p) direction. First-principles calculations indicate that different O6 octahedral rotations under strain are responsible for this phenomenon. Our work demonstrates that the extreme freedom in tuning the strain and symmetry of freestanding films opens a new fertile playground for novel strain-driven phases in transition metal oxides.