We grew high-quality single crystals of the antiferromagnet EuSn3 with the AuCu3-type cubic crystal structure by the Sn self-flux method and measured the electrical resistivity, magnetic susceptibility, high-field magnetization, specific heat, thermal expansion, and de Haas-van Alphen (dHvA) effect, in order to study the magnetic and Fermi surface properties. We observed steplike changes in the electrical resistivity and magnetic susceptibility, and a sharp peak of the specific heat and thermal expansion coefficient at a Néel temperature TN = 36.4 K. The first-order nature of the antiferromagnetic transition was ascertained by the observation of thermal hysteresis as well as of latent heat at TN. The present antiferromagnetic transition is found to be not a typical second-order phase transition but a first-order one. From the results of dHvA experiment, we clarified that the Fermi surface is very similar to that of the divalent compound YbSn3, mainly consisting of a nearly spherical hole Fermi surface and eight ellipsoidal electron Fermi surfaces. EuSn3 is possibly a compensated metal, and the occupation of a nearly spherical hole Fermi surface is 3.5% in its Brillouin zone, indicating that EuSn3 is a semimetal.