We have synthesized single crystalline samples of Gd3Co4Sn13 intermetallic compound using a Sn-flux method. This compound crystallizes with a cubic Yb3Co4Sn13-type structure, space group Pm-3n, which has 40 atoms per unit cell. Measurements of the magnetic susceptibility, heat capacity, electrical resistivity, and electron spin resonance (ESR) revealed that Gd3Co4Sn13 is a metallic Curie-Weiss paramagnet at high temperature and presents an antiferromagnetic ordering below TN=14.5K. In the paramagnetic state, a single Gd3+ ESR line with a nearly temperature independent g∼2.005(2) is observed, and its linewidth follows a Korringa-like behavior as a function of temperature. From the Korringa rate (ΔH∕ΔT∼4Oe∕K) and g-shift (Δg∼0.012) obtained from the ESR experiments combined with the magnetic susceptibility and specific heat data for Gd3Co4Sn13, we have extracted the exchange parameters between the Gd3+ local moments and the conduction-electrons (c-e) in this compound. This exchange parameter Jfs≈10meV was found to be c-e wave-vector independent and the electronic structure of Gd3Co4Sn13 has a single band character.