The electronic band structures of Metal-doped titanium dioxide, M-doped $TiO_2$ (M=Co, Cr, Fe), have been studied by using XRD, UV-vis diffuse reflectance spectrometer and FP-LAPW (Full-Potential Linearized Augmented-Plane-Wave) method. The UV-vis of M-doped $TiO_2$ (M=Co, Cr, Fe) showed two absorption edges; the main edge due to the titanium dioxide at 387 nm and a shoulder due to the doped metals at around 560 nm. The band gap energies of Co, Cr and Fe-doped $TiO_2$ calculated by FP-LAPW method were 2.6, 2.0, and 2.5 eV, respectively. The theoretically calculated band gap energy of $TiO_2$ by using FP-LAPW method was the same as experimental results. FP-LAPW method will be useful for fabrication and development of photo catalysts working under visible light.