Based on high-resolution spectra we revealed variability of the optical spectrum of the cool star identified with the IR source IRAS 20508+2011. Over the five years of our observations, the radial velocity derived from photospheric absorption lines varied in the interval V_r_=15-30km/s. In the same time, the H(alpha) profile varied from an intense bell-shaped emission line with a small absorption to 2-peaked emission with a central absorption feature below the continuum level. At all but one epoch, the positions of the metallic photospheric lines were systematically shifted relative to the H(alpha) emission: Delta V_r_=V_r_(met)-V_r_(Halpha,emis)~-23km/s. The NaD doublet lines shown a complex profile with broad (half-width about 120km/s) emission and photospheric absorption, as well as an interstellar component. We used model atmospheres to determine the physical parameters and chemical composition of the star's atmosphere: Teff=4800K, logg=1.5, Vt=4.0km/s and metallicity [Fe/H]=-0.36. We detected overabundances of oxygen [O/Fe]=+1.79 (with the ratio [C/O]~-0.9), and alpha-process elements, as well as a deficit of heavy metals. The totality of the parameters suggests that the optical component of IRAS 20508+2011 is an "O-rich" AGB star with luminosity M_v_~-3mag that is close to its evolution transition to the post-AGB stage.