We report the results on the structure, transport, and magnetic properties of a layered oxysulfide CaOFeS with a stacked triangle lattice of Fe ions. The susceptibility data show a broad maximum near 120 K, indicating the existence of two-dimensional (2D) short-range ordering in this compound. Features associated with long-range antiferromagnetic (AFM) phase transition are seen below 40 K. Meanwhile, a very small heat-capacity anomaly is detected around 35 K, and most of the measured magnetic entropy is lost during the 2D ordering process. Both crystal and magnetic structures were studied by neutron powder diffraction at 300, 125, 40, and 6 K. The structure was refined based on space group $P{6}_{3}mc$ with $a=3.759\phantom{\rule{0.28em}{0ex}}98(4)$ and $c=11.383\phantom{\rule{0.28em}{0ex}}51(16)\phantom{\rule{0.16em}{0ex}}\AA{}$ at ambient temperature. Low-temperature diffraction reveals 2D magnetic correlations between Fe moments without showing significant structural distortion. Warren peak shape analysis of the neutron-diffraction data at $2\ensuremath{\theta}$ near 18\ifmmode^\circ\else\textdegree\fi{} is employed to characterize the correlation length in the 2D magnetic state with lowering temperature. The geometrically frustrated compound is found to gradually condense into a partial long-range ordered state with AFM coupled Fe layers between 40.6 and 26 K. The resulting partially ordered magnetic structure is a $G$-type Ising AFM with a propagation vector of $\mathbf{k}=(1/2,1/2,0)$ and an ordered magnetic moment of $2.59(3){\ensuremath{\mu}}_{\mathrm{B}}/\mathrm{Fe}$ along $c$ at 6 K.