A new multi-phase lattice hydrodynamic traffic flow model is proposed by considering the effect of multi-forward looking sites on a unidirectional highway. We examined the qualitative properties of proposed model through linear as well as nonlinear stability analysis. It is shown that the multi-anticipation effect can significantly enlarge the stability region on the phase diagram and exhibit three-phase traffic flow. It is also observed that the multi-forward looking sites have prominent influence on traffic flow when driver senses the relative flux of leading vehicles. Theoretical findings are verified using numerical simulation which confirms that the traffic jam is suppressed efficiently by considering the information of leading vehicles in unidirectional multi-phase traffic flow. •A multi-phase lattice model is presented by incorporating the effect of forward looking sites.•The qualitative properties of proposed model are analyzed theoretically.•Phase diagrams are presented for different parameters.•The effect of forward leading lattices on multi-phase traffic dynamics is examined numerically.