We present experimental and theoretical investigations for the cobalt thiospinel ${\mathrm{Co}}_{3}{\mathrm{S}}_{4\ensuremath{-}\ensuremath{\delta}}$. High-quality samples of ${\mathrm{Co}}_{3}{\mathrm{S}}_{4\ensuremath{-}\ensuremath{\delta}}$ $(\ensuremath{\delta}\ensuremath{\sim}0.1)$ were prepared so as to measure their intrinsic properties. The measurements of magnetic susceptibility, specific heat, and electrical transport consistently indicate an antiferromagnetic transition at $\ensuremath{\sim}60$ K, which is attributed to long-range magnetic ordering in the $\mathrm{Co}(A)$ ($A$-site Co ions) diamond sublattice. In addition, there exists a short-range magnetic ordering at around 120 K associated with the magnetic frustrations. The high-temperature magnetic susceptibility obeys Curie-Weiss law, from which a small effective magnetic moment of $1.0\phantom{\rule{0.28em}{0ex}}{\ensuremath{\mu}}_{\mathrm{B}}$ per formula unit is yielded. The main experimental results can be interpreted by the density-functional-theory calculations with a Hubbard $U$ correction of $\ensuremath{\sim}0.5$ eV. Combining the experimental measurements with the theoretical calculations, we conclude that ${\mathrm{Co}}_{3}{\mathrm{S}}_{4}$ represents a rare example of itinerant-electron diamond-lattice antiferromagnet with moderate electron correlations.