Graphene oxide (GO) membranes are well-known materials for water purification, owing to their unique molecular transport and sieving properties. However, one of the factors that limits their use in aqueous and organic solutions for applications in industries and water treatment plants is their tendency to swell, forming an enlarged interlayer spacing that disintegrates its structure. Here we report stable ethylenediamine-cross-linked GO membranes, which can efficiently permeate water and organic solvents and filter organic solutions containing molecular dyes. The prepared membranes with a 150 nm thickness demonstrated high permeance for water and organic solvents and exhibited a rejection >95% for small organic dyes dissolved in methanol. A dead-end filtration device was used to estimate the performance of the membranes, confirming pure water permeance of 14 L m-2 h-1 bar-1. The acetone permeance was 30 L m-2 h-1 bar-1, and the N-methyl-2-pyrrolidone permeance was 5 L m-2 h-1 bar-1. At the same time, the cross linker prevented the disruption of the sheets. The combination of stability, high performance, and simplicity of fabrication make these membranes advantageous for potential application in aqueous and non-aqueous industrial separations.