We studied through V and I photometry the properties of the globular cluster systems of five early–type galaxies in the Fornax galaxy cluster : NGC 1374 , NGC 1379 , NGC 1387 , NGC 1427 , and the central giant elliptical NGC 1399 . While the four normal galaxies have between 300 and 500 globular clusters , leading to specific frequencies of 4 \pm 1 for all of them , NGC 1399 has around 6000 \pm 600 globular clusters and a specific frequency of 12 \pm 3 . The globular cluster colors are somewhat redder than those of the Milky Way globular clusters , however with a similar dispersion . This indicates a wide range of metallicities in all our galaxies with a mean metallicity somewhat higher than in the galactic halo , comparable to the galactic bulge . In NGC 1399 the dispersion is about twice as high , and the color distribution could be multi–modal . No color gradient could be detected within the sensitivity of our photometry . The density profiles of the globular cluster systems follow the galaxy light in all the galaxies . In NGC 1399 the globular cluster system is much flatter than in the other galaxies , but coincides with the large cD envelope of the galaxy . None of the globular cluster systems is clearly elongated , even the ones in NGC 1374 and NGC 1427 ( E1 and E3 respectively ) appear rather spherical . From a comparison with studied globular cluster systems in spiral galaxies , we conclude that our faint ellipticals have no more globular clusters than spirals of the same mass , and neither differ in their other properties , such as globular cluster colors and morphological properties of the system . For these galaxies there is no need to imply a different formation scenario of the globular cluster system . The central giant elliptical has far more globular clusters and show signatures of a different history in the building up of its globular cluster system .