The galaxy NGC 1275 was observed with the Hopkins Ultraviolet Telescope (HUT) during the Astro-1 space shuttle mission in 1990 December. NGC 1275 lies at the center of the Perseus cluster cooling flow and is surrounded by a bright emission-line nebula. The galaxy's far-UV spectrum shows a faint continuum and emission from Lyman α λ1216, C Iv λλ1548, 1551, and He II λ1640 at the redshift of the galaxy. The profile of the redshifted Lyα line is consistent with the multiple-component feature observed by Johnstone & Fabian with HST [MNRAS, 273,625(1995)]. The redshifted C IV line has both a broad component due to the galactic nucleus and a narrow component that we associate with the surrounding nebula. We set an upper limit on the flux of O VI λλ1032, 1038 and find that the reddening-corrected ratio I(0 VI)/I(C IV)< 1.3 is too low for a simple cooling flow, indicating that other processes must contribute to the diffuse C IV emission. The I(0 VI)/I(C IV) and I(Lyα)/I(C IV) ratios are consistent with shock velocities between ~100 and 110 km s^-1^, but the observed line luminosities cannot readily be accounted for by shock models. Models assuming either photoionization by a central source or turbulent mixing layers cannot produce the diffuse C IV emission. The continuum spectrum shows evidence of B-star emission from the high- velocity system. It is well fit by a model in which star formation has continued for at least 5 x 10^8^ yr with a Salpeter IMF at a constant rate of 30 M_sun_ yr^-1^, corresponding to a star-formation efficiency in the cooling flow of approximately 15%.