We have measured the optical conductivity σ(ω) of Yb1-xLuxB12 (0≤x≤1), where the system evolves from a Kondo semiconductor at x=0 to a nonmagnetic metal at x=1. For x=0, σ(ω) exhibits a clear energy gap with an onset at ∼20 meV and a shoulder at 38 meV. As x increases, the gap is rapidly filled in from the bottom, while the shoulder remains at ∼40 meV up to x=1/2. These results suggest that Lu substitution into YbB12 produces an in-gap band, but the characteristic energy for the gap remains unchanged in a wide range of x. Spectral evolutions of a characteristic mid-infrared peak, which results from Yb 4f-derived states near the Fermi level, suggest a strong coupling of Yb 4f electrons with conduction electrons.