We present a detailed high-resolution spectroscopic analysis of 12 red giant stars, in single and binaries or multiples systems, classified as members of the intermediate-age (631 Myr) open cluster NGC 2539. We used FEROS echelle spectra and the standard LTE analysis to derive the atmospheric parameters for the stars and the abundance ratios of light elements (Li, C, N), light odd-Z elements (Na, Al), α-elements (Mg, Si, Ca, Ti), Fe-group elements (Cr, Fe, Ni), and n-capture elements (Y, Zr, Ce, Nd, Eu). Our results show that the sample star of NGC 2539 has low projected rotational velocities and an almost solar metallicity, with a mean of [Fe/H] = −0.03 ± 0.07 dex. The abundance pattern displays for the analyzed stars are, in general, similar to those presented by solar neighborhood stars, including giant members of others open clusters. In particular, light elements and Na abundance pattern shows anomalies resulting from the appearance of enriched material on the stellar surface, produced by mechanisms like the first dredge-up and/or thermohaline and rotation-induced mixing. We also identified two of the spectroscopic binaries of our sample as 'yellow stragglers' and we determined the nature of their companions.