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We investigate theoretically the spin-dependent transport and tunnel magnetoresistance in a system consisting of two ferromagnetic graphene (FG) electrodes separated by the Thue-Morse graphene superlattice (TMGSL) or periodic graphene superlattice (PGSL). Using transfer matrix methods, the spin-dependent conductance, tunnel magnetoresistance, and spin polarization of current of the FG/TMGSL/FG junctions are numerically calculated and compared with those of the FG/PGSL/FG junctions. The results indicate that all the physical quantities considered here show typical quasiperiodic oscillations as the electrostatic barrier height increases. Furthermore, the conductances, spin polarization of the current for the parallel configuration of magnetization, and tunnel magnetoresistance monotonically increase or decrease with increasing exchange splitting energy. Interestingly, compared to the FG/PGSL/FG junctions, all the physical quantities, considered here, of the FG/TMGSL/FG junctions can exhibit a more marked growth stage effect, along with stronger and more irregular oscillations with increasing electrostatic barrier height.