We present a library of 1654 high-resolution stellar spectra, with a sampling of 0.3 Åand covering the wavelength range from 3000 to 7000 Å. The library was computed with the latest improvements in stellar atmospheres, incorporating non-local thermodynamic equilibrium (non-LTE) line-blanketed models for hot, massive (Teff>= 27500K) and line-blanketed models for cool (3000 <=Teff<= 4500K) stars. The total coverage of the grid is 3000 K <=Teff<= 55000 K and -0.5 <= log g<= 5.5, for four chemical abundance values: twice solar, solar, half solar and 1/10 solar. Evolutionary synthesis models using this library are presented in a companion paper. We tested the general behaviour of the library by calculating and comparing equivalent widths of numerous H and HeI lines, and some of the commonly used metallic indices. We also compared the library with the empirical libraries STELIB and Indo-US. The full set of the synthetic stellar spectra is available from our websites (http://www.iaa.csic.es/~rosa and http://www.astro.iag.usp.br/~lucimara/library.htm).