In this study composite mixed matrix membranes containing hydrophilic microphase-separated block copolymer (Pebax (R) 1657) and graphene oxide nanosheets were prepared using a dip coating method. Water vapor and N-2 gas permeation were measured as a function of different parameters: (i) layer thickness, (ii) content of graphene oxide (GO), and (iii) content of reduced GO. Surprisingly, a concentration of only 2 wt% of GO nanosheets well dispersed in the Pebax layer boosted the selectivity 8 times by decreasing the water vapor permeance by only 12% whereas N-2 gas permeance decreased by 70%. Using reduced GO instead, the water vapor permeance declined by up to 16% with no influence on the N-2 gas permeance. We correlated the permeation properties of the mixed matrix membranes with different models and found, that both the modified Nielsen model and the Cussler model give good correlation with experimental findings.