We have studied the O and Ne absorption features in the X-ray spectrum of Cyg X-2 observed with the Chandra LETG. The O absorption edge is represented by the sum of three absorption-edge components within the limit of the energy resolution and the photon counting statistics. Two of them are due to the atomic O; their energies correspond to two distinct spin states of photo-ionized O atoms. The remaining edge component is considered to represent compound forms of oxide dust grains. Since Cyg X-2 is about 1.4 kpc above the galactic disk, the H column densities can be determined by radio (21 cm and CO emission line) and H alpha observations with relatively small uncertainties. Thus the O abundance relative to H can be determined from the absorption edges. We found that the dust scattering can affect the apparent depth of the edge of the compound forms. We determined the amplitude of the effect, which we consider is the largest possible correction factor. The ratio of column densities of O in atomic to compound forms and the O total abundance were respectively determined to be in the range 1.7^{+3.0}_{-0.9} to 2.8^{+5.1}_{-1.5} (ratio), and 0.63 +/- 0.12 solar to 0.74 +/- 0.14 solar (total), taking into account the uncertainties in the dust-scattering correction and in the ionized H column density. We also determined the Ne abundance from the absorption edge to be 0.75 +/- 0.20 solar. These abundance values are smaller than the widely-used solar values but consistent with the latest estimates of solar abundance.
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