A perovskite La_0.59±0.01Li_0.27±0.01TiO_3.02±0.02 single crystal was grown by the floating zone method and its lithium ion conductivity was measured. The conductivity was found to be predominantly ionic. The ionic conductivities at 300K parallel and perpendicular to the c-axis are 5.8×10^-4 and 6.8×10^-4S·cm^-1, respectively. The anisotropy of the ionic conductivity corresponds to that of the structure, i.e., of the distribution of La ions. Furthermore, the ionic conductivity and activation energy for ion conduction are almost the same as those of a grain in polycrystalline samples, indicating that the evaluation of the ionic conductivity of polycrystalline samples was appropriate.