  We present a scheme to obtain anti-chiral edge states in an exciton-polariton
honeycomb lattice with strip geometry, where the modes corresponding to both
edges propagate in the same direction. Under resonant pumping the effect of a
polariton condensate with nonzero velocity in one linear polarization is
predicted to tilt the dispersion of polaritons in the other, which results in
an energy shift between two Dirac cones and the otherwise flat edge states
become tilted. Our simulations show that due to the spatial separation from the
bulk modes the edge modes are robust against disorder.
