  We present a new $6D$ infinite spin field theory in the light-front
formulation. The Lorentz-covariant counterparts of these fields depend on
6-vector coordinates and additional spinor variables. Casimir operators in this
realization are found. We obtain infinite-spin fields in the light-cone frame
which depend on two sets of the $\mathrm{SU}(2)$-harmonic variables. The
generators of the $6D$ Poincar\'e group and the infinite spin field action in
the light-front formulation are presented.
