We performed a non-local thermodynamic equilibrium (NLTE) analysis of the infrared oxygen triplet for a large number of Cepheid spectra obtained with the Hobby-Eberly Telescope. These data were combined with our previous NLTE results for stars observed with the Max Planck Gesellschaft Telescope with the aim of investigating the oxygen abundance distribution in the Galactic thin disc. We found the slope of the radial (O/H) distribution to be equal -0.058dex/kpc. However, we found some evidence that the distribution might become flatter in the outer parts of the disc. This is supported by the results of other authors who have studied open clusters, planetary nebulae and Hii regions. Some mechanisms of flattening are discussed.