At the distance of NGC 5128 (3.6+/-0.2Mpc) it is possible to resolve globular clusters with high resolution imaging from the ground, thus allowing the globular cluster candidate selection primarily through their morphological properties. I report the discovery of 71 globular clusters in NGC 5128 on VLT UT1+FORS1 images, including the faintest members (M_V_~-5) known to date in this galaxy as well as in 5 previously-known clusters. U- and V-band photometry has been measured for all the candidates and the luminosity function, spanning -10.1<M_V_<-4.9 and -9.3<M_U_<-3.3, constructed. These are the deepest globular cluster luminosity functions in an elliptical galaxy determined so far. The Kolmogorov-Smirnov statistics show that the difference between the globular cluster luminosity functions of NGC 5128 and the Milky Way is not larger than the difference between the ones of M 31 and the Milky Way. The (U-V)_0_ color histogram shows a bimodal distribution. For 23 globular clusters I obtained K-band images with SOFI at the NTT in La Silla. Their positions in the (U-V) vs. (V-K) color-color diagram indicate that they are indeed old globular clusters. Assuming that the globular clusters in NGC 5128 span a similar age range as the ones in the Milky Way and adopting a linear fit between the metallicity and (U-V)0 color, the metal-rich clusters peak at [Fe/H]=-0.6dex and the metal-poor ones peak at [Fe/H]=-1.7dex.