Charge transport in a solid-state dye-sensitized solar cell is investigated. Unexpectedly, hole transport in the organic component (Spiro-MeOTAD) is faster than the electron transport in the inorganic component (TiO2). The electron mobility or diffusion coefficient through TiO2 does not increase with increasing illumination intensity, as would be predicted by the multitrapping model for electron transport. The results highlight that poor electron transport in TiO2 is a key issue for further improvements in device performance.