We have investigated the electronic structure of the quasi-one-dimensional organic metal TTF-TCNQ by measuring Compton scattering from single crystals. The measured profiles are significantly anisotropic. The directional anisotropies were compared with those derived by two different theoretical approaches. The first is the molecular orbital approximation: Compton profiles were calculated for the TTF and TCNQ molecules, separately, and then these were superposed. In spite of the simplicity of this approach, the agreement is reasonably good, implying that the electronic wave functions of TTF and TCNQ in the crystal are not very different from those of isolated molecules. The second approach is an ab initio pseudopotential band-structure calculation. The agreement is better, presumably due to the more accurate description of the crystallinity (including, for example, the inter-molecule charge transfer and band formation).