Multiple molecular lines with radiative transfer modeling are a powerful tool to probe the physics of star-forming gas in galaxies. We investigate the gas properties in the center of spiral galaxy NGC 2903 using low- J CO lines, i.e. (CO)-C-12(1-0), (CO)-C-12(2-1), (CO)-C-12(3-2), (CO)-C-13(1-0), and HCN(1-0). We apply a nonlocal thermodynamic equilibrium radiative transfer code to derive beam-averaged molecular gas properties. We use two methods (i.e. chi(2) minimization and likelihood) to define the best model representing the observed line ratios best. The line ratio diagnostics suggest that CO gas in the center of NGC 2903 is thinner and the dense gas fraction is similar compared to that of spirals, starbursts, and early-type galaxies (ETGs), while the gas in the center of the galaxy is warmer than that of ETGs and colder than that of starbursts. Based on the best-fitting model results, we find that the beam-averaged gas kinetic temperature is T-K = 20 K, H-2 volume number density is log(n (H-2)) = 4.2 cm(-3), and CO column number density is log( N (CO)) = 19.0 cm(-2) in the center of NGC 2903. Both methods, i.e. the line ratio diagnostics and modeling, indicate an ISM in the center of NGC 2903 having intermediate temperature and star formation activity (also supported by star formation rates), thinner CO gas with similar dense gas fraction, and higher H-2 volume number density compared to that of spirals, ETGs, and starbursts.