Motivated by the possible non-spin-singlet superconductivity in the magic-angle twisted trilayer graphene experiment, we investigate the triplet-pairing superconductivity arising from a correlationinduced spin-fermion model of Dirac fermions with spin, valley, and sublattice degrees of freedom. We find that the f-wave pairing is favored due to the valley-sublattice structure, and the superconducting state is time-reversal symmetric, fully gapped, and nontopological. With a small in-plane magnetic field, the superconducting state becomes partially polarized, and the transition temperature can be slightly enhanced. Our results apply qualitatively to Dirac fermions for the triplet-pairing superconductivity in graphene-based moire systems, which is fundamentally distinct from triplet superconductivity in 3He and ferromagnetic superconductors.