We present the first results of a positron two-dimensional angular correlationof annihilation radiation (2D-ACAR) experiment on a typical organic conductor tetrathiofulvalinium tetracyanoquinodimethan (TTF-TCNQ). Although the observed spectrum is relatively smooth, we have succeeded inextracting the anisotropy reflecting the electronic structure of TTF-TCNQ. In order to clarify the origin of the anisotropy, we have performed theoretical simulations. Electron wave functions are expressed as TTF or TCNQ molecular orbitals obtained by self-consistent quantum chemical calculations (GAUSSIAN92) while the positron wave function is calculated by the superposed atom method. The simulated 2D-ACAR spectrum is in reasonable agreement with the experimental one. This implies that the predominant features observed can be interpreted in terms of molecular orbitals.