We present the results of a series of Chandra observations of globular cluster (GC) X-ray sources in M31. Among some 20 GC X-ray sources detected in our M31 observations, 2-3 of them show super-Eddington luminosity (> 1038 erg s-1). It is an interesting fact that the highest X-ray luminosities achieved by Galactic GCs are only several times 1037 erg s-1, and that none are black hole candidates. There are several possible explanations for such a large luminosity: 1) there are multiple sources; 2) the source is a black hole; 3) the flux is beamed. In addition, metallicity can account for higher luminosities than the standard Eddington limit. Some of the M31 GC X-ray sources are also variables and show transient behavior. By combining all the available archival data, we compare the properties of these sources to those Galactic GC X-ray sources.