The electromagnetic and gravitational form factors of decuplet baryons are systematically studied with a covariant quark–diquark approach. The model parameters are firstly discussed and determined through comparison with the lattice calculation results integrally. Then, the electromagnetic properties of the systems including electromagnetic radii, magnetic moments, and electric-quadrupole moments are calculated. The obtained results are in agreement with experimental measurements and the results of other models. Finally, the gravitational form factors and the mechanical properties of the decuplet baryons, such as mass radii, energy densities, and spin distributions, are also calculated and discussed.