In this work, graphene aerogel (GA) decorated with Fe3O4@SiO2@Pd nanoparticles (GA-FSNP@Pd) as a novel three-dimensional graphene-magnetic palladium nanohybrid catalyst. This catalyst showed high catalytic activity for the Suzuki and Heck cross-coupling reactions. This noteworthy catalyst activity can be due to the high dispersion of FSNP@Pd nanoparticles on GA. The nanohybrid exhibits an interconnected mesoporous framework of graphene sheets with uniform dispersion of FSNP@Pd nanoparticles. Interestingly, the catalyst could be recovered in a facile manner from the reaction mixture and recycled ten times without appreciable loss of activity. High yield, low reaction time, magnetic separation and non-toxicity of the nanohybrid catalyst are the main merits of this protocol. [GRAPHICS] .