A high resolution spectroscopic observation of the red supergiant star RM_1-390 in the Large Magellanic Cloud was made from a 3.6 m telescope at the European Southern Observatory. Spectral resolving power was R=20,000, with a signal-to-noise ratio S/N > 100. We found the atmospheric parameters of RM_1-390 to be as follows: the effective temperature Teff = 4,250 ± 50 K, the surface gravity log g = 0.16 ± 0.1, the microturbulent velocity vmicro = 2.5 km/s, the macroturbulence velocity vmacro = 9 km/s and the iron abundance [Fe/H] = -0.73 ± 0.11. The abundances of 18 chemical elements from silicon to thorium in the atmosphere of RM_1-390 were found using the spectrum synthesis method. The relative deficiencies of all elements are close to that of iron. The fit of abundance pattern by the solar system distribution of r- and s-element isotopes shows the importance of the s-process. The plot of relative abundances as a function of second ionization potentials of corresponding chemical elements allows us to find a possibility of convective energy transport in the photosphere of RM_1-390.