We present homogeneous and accurate iron abundances for almost four dozen ( 47 ) of Galactic Cepheids using high–spectral resolution ( R \sim 40,000 ) high signal–to–noise ratio ( SNR \geq 100 ) optical spectra collected with UVES at VLT . A significant fraction of the sample ( 32 ) is located in the inner disk ( R { } _ { G } \leq 6.9 kpc ) and for half of them we provide new iron abundances . Current findings indicate a steady increase in iron abundance when approaching the innermost regions of the thin disk . The metallicity is super–solar and ranges from 0.2 dex for R { } _ { G } \sim 6.5 kpc to 0.4 dex for R { } _ { G } \sim 5.5 kpc . Moreover , we do not find evidence of correlation between iron abundance and distance from the Galactic plane . We collected similar data available in the literature and ended up with a sample of 420 Cepheids . Current data suggest that the mean metallicity and the metallicity dispersion in the four quadrants of the Galactic disk attain similar values . The first–second quadrants show a more extended metal-poor tail , while the third–fourth quadrants show a more extended metal–rich tail , but the bulk of the sample is at solar iron abundance . Finally , we found a significant difference between the iron abundance of Cepheids located close to the edge of the inner disk ( [ Fe/H ] \sim 0.4 ) and young stars located either along the Galactic Bar or in the Nuclear Bulge ( [ Fe/H ] \sim 0 ) . Thus suggesting that the above regions have had different chemical enrichment histories . The same outcome applies to the metallicity gradient of the Galactic Bulge , since mounting empirical evidence indicates that the mean metallicity increases when moving from the outer to the inner Bulge regions .