Ab initio calculations of lithium diffusion into titanium dioxide in the form of rutile are presented. An analysis of the site preference for intercalation and diffusion pathways of Li-ions is performed. The expansion of the host structure on Li-insertion is found to contribute to the enhanced diffusion of Li-ions along the tetragonal c direction. At the same time, a large distortion of the rutile framework makes Li diffusion in the ab planes prohibitively slow. Anisotropy of Li diffusion is used to explain the observed electrochemical behaviour of rutile. Computed diffusion coefficients were found in excellent agreement with the measured values.