FIREBall (Faint Intergalactic Redshifted Emission Balloon) had a successful first engineering flight in July of 2007 from Palestine, Texas. Here we detail the design and construction of the spectrograph. FIREBall consists of a 1m telescope coupled to a fiber-fed ultraviolet spectrograph flown on a short duration balloon. The spectrograph is designed to map hydrogen and metal line emission from the intergalactic medium at several redshifts below z=1, exploiting a small window in atmospheric oxygen absorption at balloon altitudes. The instrument is a wide-field IFU fed by almost 400 fibers. The Offner mount spectrograph is designed to be sensitive in the 195-215nm window accessible at our altitudes of 35-40km. We are able to observe Lyα, as well as OVI and CIV doublets, from 0.3 < z < 0.9. Observations of UV bright B stars and background measurements allow characterization of throughput for the entire system and will inform future flights.