Many organic metals display exotic properties such as superconductivity, spin-charge separation and so on and have been described as quasi-one-dimensional Luttinger liquids. However, a genuine Fermi liquid behaviour with quasiparticles and Fermi surfaces have not been reported to date for any organic metal. Here, we report the experimental Fermi surface and band structure of an organic metal (BEDT-TTF)(3)Br(pBIB) obtained using angle-resolved photoelectron spectroscopy, and show its consistency with first-principles band structure calculations. Our results reveal a quasiparticle renormalization at low energy scales (effective mass m*=1.9 m(e)) and ω(2) dependence of the imaginary part of the self energy, limited by a kink at ~50 meV arising from coupling to molecular vibrations. The study unambiguously proves that (BEDT-TTF)(3)Br(pBIB) is a quasi-2D organic Fermi liquid with a Fermi surface consistent with Shubnikov-de Haas results.