The present disclosure relates to a process to produce aqueous dispersions of graphene stabilized by cellulose, offering an alternative to the current methods of dispersion of graphene. The present process provides the advantages that it uses biodegradable cellulose compatible with the environment and can be used in industrial processes in alkaline medium or in the absence of alkali; and when graphene is stabilized with cellulose in alkaline medium it becomes unstable when in contact with natural waters, thus precipitating and being easily removed or concentrated. In other embodiments, solids obtained by drying of the dispersions, once dried, can be redispersed in aqueous alkaline solution.