We analyse for the first time the radial abundance gradients of the disc stars of a disc galaxy simulated with our three-dimensional, fully cosmological chemodynamical galaxy evolution code GCD+. We study how [Fe/H], [N/O], [O/Fe], [Mg/Fe] and [Si/Fe] vary with galactocentric radius. For the young stars of the disc, we found a negative slope for [Fe/H] and [N/O] but a positive [O/Fe], [Mg/Fe] and [Si/Fe] slope with radius. By analysing the star formation rate at different radii, we found that the simulated disc contains a greater fraction of young stars in the outer regions, while the old stars tend to be concentrated in the inner parts of the disc. This can explain the positive [α/Fe] gradient as well as the negative [N/O] gradient with radius. This radial trend is a natural outcome of an inside-out formation of the disc, regardless of its size and can thus explain the recently observed positive [α/Fe] gradients in the Milky Way disc open clusters.