Based on the first-principles calculations, we have investigated the geometry, binding properties, density of states and band structures of the novel superconductor LaFe1-xCoxAsO and its parent compounds with the ZrCuSiAs structure. We demonstrate that La-O bond and TM-As (TM=Fe or Co) bond are both strongly covalent, while the LaO and TMAs layers have an almost ionic interaction through the Bader charge analysis. Partial substitution of iron with cobalt modify the Fermi level from a steep edge to a flat slope, which explains why in this system Co doping suppresses the spin density wave (SDW) transition.