We present Utrecht Echelle Spectrograph@William Herschel Telescope high-resolution spectra of the low-mass X-ray binary (LMXB) Cygnus X-2. We have derived the stellar parameters of the secondary star using χ2 minimization procedure, and taking into account any possible veiling from the accretion disc. We determine a metallicity higher than solar ([Fe/H] = 0.27 ± 0.19), as seen also in the neutron star X-ray binary Centaurus X-4. The high quality of the secondary's spectrum allow us to determine the chemical abundances of O, Mg, Si, Ca, S, Ti, Fe, and Ni. We found that some α-elements (Mg, Si, S, Ti) are enhanced, consistent with a scenario of contamination of the secondary star during the supernova event. Surprisingly oxygen appears to be underabundant, whereas enhanced abundances of Fe and Ni are measured. Assuming that these abundances come from matter that has been processed in the SN and then captured by the secondary star, we explore different SN explosion scenarios with diverse geometries. A non-spherically symmetric SN explosion, with a low mass cut, seems to reproduce better the observed abundance pattern of the secondary star compared to the spherical case.