In this work we present a grid of LTE and non-LTE synthetic spectra of hot DA white dwarfs (WDs). In addition to its usefulness for the determination of fundamental stellar parameters of isolated WDs and in binaries, this grid will be of interest for the construction of theoretical libraries for stellar studies from integrated light. The spectral grid covers both a wide temperature and gravity range, with 17000K<=Teff<=100000K and 7.0<=log(g)<=9.5. The stellar models are built for pure hydrogen and the spectra cover a wavelength range from 900{AA} to 2.5um. Additionally, we derive synthetic HST/ACS, HST/WFC3, Bessel UBVRI, and SDSS magnitudes. The grid was also used to model integrated spectral energy distributions of simple stellar populations and our modeling suggests that DAs might be detectable in ultraviolet bands for populations older than ~8Gyr.