We have conducted an LTE abundance analysis for SAO 40039, a warm post-AGB star whose spectrum is known to show surprisingly strong HeI lines for its effective temperature and has been suspected of being H-deficient and He-rich. High-resolution optical spectra are analyzed using a family of model atmospheres with different He/H ratios. Atmospheric parameters are estimated from the ionization equilibrium set by neutral and singly ionized species of Fe and Mg, the excitation of FeI and FeII lines, and the wings of the Paschen lines. On the assumption that the HeI lines are of photospheric and not chromospheric origin, a He/H ratio of approximately unity is found by imposing the condition that the adopted He/H ratio of the model atmosphere must equal the ratio derived from the observed HeI triplet lines at 5876, 4471, and 4713{AA}, and singlet lines at 4922 and 5015{AA}. Using the model with the best-fitting atmospheric parameters for this He/H ratio, SAO 40039 is confirmed to exhibit mild dust-gas depletion, i.e., the star has an atmosphere deficient in elements of high condensation temperature. The star appears to be moderately metal-deficient with [Fe/H]=-0.4dex. But the star's intrinsic metallicity as estimated from Na, S, and Zn, elements of a low condensation temperature, is [Fe/H]_o_~-0.2 ([Fe/H]_o_ refers to the star's intrinsic metallicity). The star is enriched in N and perhaps O as well, changes reflecting the star's AGB past and the event that led to He enrichment.