GN-z11 was photometrically selected as a luminous star-forming galaxy candidate at redshift z > 10 based on Hubble Space Telescope (HST) imaging data. Follow-up HST near-infrared grism observations detected a continuum break that was explained as the Ly-alpha break corresponding to z = 11.09 (+0.08-0.12). However, its accurate redshift remained unclear. Here we report a probable detection of three ultraviolet (UV) emission lines from GN-z11, which can be interpreted as the [C III] 1907, C III] 1909 doublet and O III] 1666 at z = 10.957+/-0.001 (when the Universe was only ~420 Myr old, or ~3% of its current age). This is consistent with the redshift of the previous grism observations, supporting GN-z11 as the most distant galaxy known to date. Its UV lines likely originate from dense ionized gas that is rarely seen at low redshifts, and its strong [C III] and C III] emission is partly due to an active galactic nucleus (AGN) or enhanced carbon abundance. GN-z11 is luminous and young, yet moderately massive, implying a rapid build-up of stellar mass in the past. Future facilities will be able to find the progenitors of such galaxies at higher redshift and probe the cosmic epoch in the beginning of re-ionization.