Single crystals of silicon doped LiFePO4 with a silicon content of 1% are grown successfully by the floating zone technique and characterized by single-crystal and powder X-ray diffraction, secondary ion mass spectroscopy, and chemical analysis. Electron paramagnetic resonance demonstrates the presence of only Fe2+; no traces of Fe3+ are found. Impedance spectroscopy as well as step-function polarization/depolarization (DC) measurements are carried out using the cells Ti/LiFe(Si)PO4/Ti and LiAl/LiI/LiFe(Si)PO4/LiI/LiAl. The electronic and ionic conductivities as well as the Li-diffusivity of the sample in the major crystallographic directions ([h00], [0k0], and [00l]) are determined. Within experimental error the transport properties along the b- and c-axes are found to be the same but differ significantly from the a-axis, which exhibits lower values. Compared to undoped LiFePO4, Si-doping leads to an increase of the ionic conductivity while the electronic conductivity decreases, which is in agreement with a donor effect. The activation energies of conductivities and diffusivities are interpreted in terms of defect chemistry and relevant Brouwer diagrams are given.