The atomic and electronic structures together with the optical properties of TiAu in the low-temperature B19 and Bll phases are calculated by using first principles local density functional approaches. Our results show that the Bll structure is more stable than B19 for the TiAu alloy in ordered equiatomic composition (Ti:Au =50:50). At Iow temperatures, the Bll structure should exist as a binary alloy from the energetic consideration.The accurate atomic positions in the unit cell have been given by fully force relaxed calculations. The calculated optical conductivities of B19 and Bll phases show a drastic change in the region of 1.5 to 3.5 e V.