Distant luminous quasars provide important information on the growth of the first supermassive black holes, their host galaxies and the epoch of reionization. The identification of quasars is usually performed through detection of their Lyman-α line redshifted to 0.9 microns at z > 6.5. Here, we report the discovery of a very Lyman-α luminous quasar, PSO J006.1240 + 39.2219 at redshift z = 6.618, selected based on its red colour and multi-epoch detection of the Lyman-α emission in a single near-infrared band. The Lyman-α line luminosity of PSO J006.1240 + 39.2219 is unusually high and estimated to be 0.8 × 1012 Solar luminosities (about 3% of the total quasar luminosity). The Lyman-α emission of PSO J006.1240 + 39.2219 shows fast variability on timescales of days in the quasar rest frame, which has never been detected in any of the known high-redshift quasars. The high luminosity of the Lyman-α line, its narrow width and fast variability resemble properties of local Narrow-Line Seyfert 1 galaxies which suggests that the quasar is likely at the active phase of the black hole growth accreting close or even beyond the Eddington limit.