Atmospheric parameters and elemental abundances of metal-poor Population II star TYC5594-576-1 ([Fe/H] = –2.8) have been studied, including the elements of neutron (n-) capture processes, as an important part of the enrichment sources of early Galaxy. Na, Mg, Al, Co, Sr, Y, Zr, Mo, Ba, La, Ce, Pr, Sm, Eu, Gd, Dy, Os, and Th abundances were determined using the synthetic spectrum method, taken into account the hyperfine structure (HFS) for the Ba II, La II and Eu II lines. The abundances of Si, Ca, Sc, N were determined based on the equivalent widths of their lines. The carbon abundance was obtained by the molecular synthesis fitting for the CH region of 4300-4330 ÅÅ. For the abundances determinations of C, Na, Mg, Al, Ba, and Th the NLTE corrections have been applied.We have determined the abundances of several n- capture elements for the first time and found that the behaviour of these elements abundances shows a significant trend with increasing atomic number. The elements ratios of [Eu/Fe] = 1.85, [Ba/Eu] = –1.24, [Sr/Ba] = –1.04 confirm the status of TYC5594-576-1 as a r-process enrichment star, with lower strontium [Sr/Fe] = –0.33 and higher thorium [Th/Fe] = 1.28 abundances. The obtained europium and thorium excesses testifies to the early enrichment of the Galaxy by the r-process elements as a result of the merger of neutron stars or black holes. The carbon abundance confirms the effect of canonical additional mixing in this star.