© ESO, 2015. We use the GALEX data of the GUViCS survey to construct the near-ultraviolet (NUV) luminosity function of the Virgo cluster over ~300 deg2, an area covering the cluster and its surrounding regions up to ~1.8 virial radii. The NUV luminosity function is also determined for galaxies of different morphological types and NUV-i colours, and for the different substructures within the cluster. These luminosity functions are robust vs. statistical corrections since based on a sample of 833 galaxies mainly identified as cluster members with spectroscopic redshift (808) or high-quality optical scaling relations (10). We fit these luminosity functions with a Schechter function, and compare the fitted parameters with those determined for other nearby clusters and for the field. The faint end slope of the Virgo NUV luminosity function (a =-1.19), here sampled down to ~NUV =-11.5 mag, is significantly flatter than the value measured in other nearby clusters and similar to the field value. Similarly, M a- =-17.56 is one to two magnitudes fainter than measured in Coma, A1367, the Shapley supercluster, and the field. These differences seem to be due to the quite uncertain statistical corrections and the small range in absolute magnitude sampled in these clusters. We do not observe strong systematic differences in the overall NUV luminosity function of the core of the cluster with respect to that of its periphery. We note, however, that the relative contribution of red and blue galaxies at the faint end is inverted, with red quiescent objects dominating the core of the cluster and star forming galaxies dominating beyond one virial radius. This observational evidence is discussed in the framework of galaxy evolution in dense environments.