We grew single crystals of U6Co by the self-flux method and measured the magnetic susceptibility, resistivity, and specific heat. The magnetic susceptibility shows very small anisotropy and weak temperature dependence, indicating small spin-susceptibility. Superconductivity was clearly observed in the resistivity, susceptibility, and specific heat at Tc~2.3K. The upper critical field was remarkably large, 7.9 and 6.6T for H ||  and , respectively, in the tetragonal structure, indicating that the ellipsoidal Fermi surface is slightly suppressed along the  direction according to the effective mass model. The specific heat shows a large jump at Tc with Delta C/gamma Tc = 1.58, and the field dependence of the specific heat at low temperatures shows an almost linear increase. These experimental results are well explained by the BCS model in the dirty limit condition. U6Co is most likely a conventional s-wave superconductor with a full superconducting gap.