Exoplanets with relatively clear atmospheres are prime targets for detailed studies of chemical compositions and abundances in their atmospheres. Alkali metals have long been suggested to exhibit broad wings due to pressure broadening, but most of the alkali detections only show very narrow absorption cores, probably because of the presence of clouds. We report the strong detection of the pressure-broadened spectral profiles of Na, K, and Li absorption in the atmosphere of the super-Neptune WASP-127b, at 4.1σ, 5.0σ, and 3.4σ, respectively. We performed a spectral retrieval modeling on the high-quality optical transmission spectrum newly acquired with the 10.4 m Gran Telescopio Canarias (GTC), in combination with the re-analyzed optical transmission spectrum obtained with the 2.5 m Nordic Optical Telescope (NOT). By assuming a patchy cloudy model, we retrieved the abundances of Na, K, and Li, which are super-solar at 3.7σ for K and 5.1σ for Li (and only 1.8σ for Na). We constrained the presence of haze coverage to be around 52%. We also found a hint of water absorption, but cannot constrain it with the global retrieval owing to larger uncertainties in the probed wavelengths. WASP-127b will be extremely valuable for atmospheric characterization in the era of James Webb Space Telescope. The reduced spectra and the narrow-band light-curves are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/616/A145