Context. The population of near-Earth asteroids (NEAs) shows a large variety of objects in terms of physical and dynamical properties. They are subject to planetary encounters and to strong solar wind and radiation effects. Their study is also motivated by practical reasons regarding space exploration and long-term probability of impact with the Earth. Aims: We aim to spectrally characterize a significant sample of NEAs with sizes in the range of 0.25-5.5 km (categorized as large), and search for connections between their spectral types and the orbital parameters. Methods: Optical spectra of NEAs were obtained using the Isaac Newton Telescope (INT) equipped with the IDS spectrograph. These observations are analyzed using taxonomic classification and by comparison with laboratory spectra of meteorites. Results: A total number of 76 NEAs were observed. We spectrally classified 44 of them as Q/S-complex, 16 as B/C-complex, eight as V-types, and another eight belong to the remaining taxonomic classes. Our sample contains 27 asteroids categorized as potentially hazardous and 31 possible targets for space missions including (459872) 2014 EK24, (436724) 2011 UW158, and (67367) 2000 LY27. The spectral data corresponding to (276049) 2002 CE26 and (385186) 1994 AW1 shows the 0.7 μm feature which indicates the presence of hydrated minerals on their surface. We report that Q-types have the lowest perihelia (a median value and absolute deviation of 0.797 ± 0.244 AU) and are systematically larger than the S-type asteroids observed in our sample. We explain these observational evidences by thermal fatigue fragmentation as the main process for the rejuvenation of NEA surfaces. Conclusions: In general terms, the taxonomic distribution of our sample is similar to the previous studies and matches the broad groups of the inner main belt asteroids. Nevertheless, we found a wide diversity of spectra compared to the standard taxonomic types. All optical data from INT are only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (ftp://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/627/A124