We construct a composite quasar spectrum from 284 HST FOS spectra of 101 quasars with redshifts z > 0.33. The spectrum covers the wavelengths between 350 and 3000 Angstrom in the rest frame, with a peak S/N level of similar to 130 per Angstrom at similar to 1200 Angstrom. Since similar to 90% of the sample quasars have redshift z < 1.5, the spectrum is suitable for studying the wavelength region shortward of Ly alpha without large effects from intervening Ly alpha forest absorption. Data in the waveband between 350 and 600 Angstrom are mainly from the spectra of z > 1.5 quasars, for which significant corrections for the accumulated Lyman-series line and continuum absorption have been applied. There is a significant steepening of the continuum slope around 1050 Angstrom. The continuum between 1050 and 2200 Angstrom can be modeled as a power law f(v) proportional to v(alpha) with alpha = -0.99 +/- 0.05. For the full sample the power-law index in the extreme ultraviolet (EUV) between 350 and 1050 Angstrom is alpha = -1.96 +/- 0.15. For the radio-loud subsample (60 objects), the EUV spectral index is alpha similar or equal to -2.2, while for the radio-quiet subsample (41 objects) it is alpha similar or equal to -1.8. The continuum flux in the wavelengths near the Lyman limit shows a depression of similar to 10%. The break in the power-law index and the slight depression of the continuum near the Lyman limit are features expected in Comptonized accretion-disk spectra. Comptonization produces a power-law tail in the wavelength band shortward of similar to 1000 Angstrom and smears out the Lyman-limit edge of the intrinsic accretion-disk spectrum. In the EUV waveband, we detect several possible emission features, including one around 690 Angstrom, that may be O III + N III produced by the Bowen fluorescence effect. Comparing our composite spectrum with one made at higher redshifts by Francis et al., we find that the equivalent widths of Ly alpha and high-ionization emission lines are larger in our sample, reflecting a known luminosity dependence. The equivalent widths of low-ionization lines do not exhibit such a dependence, suggesting that the quasar EUV continuum above similar to 50 eV is steeper at higher luminosity. Radio-quiet quasars appear to show a slightly harder continuum and lower ionization levels in their emission lines.