  In this work, the electromagnetic and gravitational form factors of a
spin-$3/2$ particle, $\Delta$ resonance, are simultaneously calculated with the
help of a relativistic covariant quark-diquark approach. The two kinds of form
factors are separately extracted from the matrix elements of the
electromagnetic current and of the energy-momentum tensor of the system. Our
numerical results show that the approach can well reproduce the electromagnetic
monopole, dipole, quadrupole, and octupole form factors comparing to the
Lattice calculations. Our obtained electromagnetic moments are also comparable
with some other approaches. Moreover, the obtained gravitational form factors,
which give the mechanical properties of the system like the mass and spin
distributions, are also displayed for the $\Delta$ isobar. In addition, some
discussions of the sign and the interpretation of the D-term are particularly
given.
