Open clusters are very useful examples to explain the constraint of the nucleosynthesis process with the luminosities of stars because the distances of the clusters are better known than those of field stars. We carried out a detailed spectroscopic analysis to derive the chemical composition of two red giants in the young open cluster NGC 5822, NGC 5822-2, and NGC 5822-201. We obtained abundances of C, N, O, Na, Mg, Al, Ca, Si, Ti, Ni, Cr, Y, Zr, La, Ce, and Nd. The atmospheric parameters of the studied stars and their chemical abundances were determined using high-resolution optical spectroscopy. We employed the local thermodynamic equilibrium model atmospheres of Kurucz and the spectral analysis code MOOG. The abundances of the light elements were derived using the spectral synthesis technique. We found that NGC 5822-2 and -201 have, respectively, a mean overabundance of the elements created by the s-process, "s," with the notation [s/Fe] of 0.77+/-0.12 and 0.83+/-0.05. These values are higher than those for field giants of similar metallicity. We also found that NGC 5822-2 and -201 have, respectively, luminosities of 140L_{sun}_ and 76L_{sun}_, which are much lower than the luminosity of an asymptotic giant branch star. We conclude that NGC 5822-2 and NGC 5822-201 are two new barium stars first identified in the open cluster NGC 5822. The mass transfer hypothesis is the best scenario to explain the observed overabundances.