  The $w_{1+\infty}$ symmetry algebra appears in the Einstein--Yang--Mills
theory, proposed recently by Strominger. In this paper, we derive the
supersymmetric $w_{1+\infty}$ symmetry by using the known results on the
operator product expansions (OPEs) between the graviton, gravitino, gluon, and
gluino in the supersymmetric version of the above theory. We calculate the four
additional commutator relations between the soft currents explicitly. In
addition, we analyze the works of Odake et al. and Pope et al. and introduce
the additional symmetry current that corresponds to the celestial gluino
operator. Through this procedure, all seven commutator relations can be
connected to the ones associated with the supersymmetric $w_{1+\infty}$ algebra
with $SU(N)$ symmetry under the restrictions of wedge modes.
