The lattice Boltzmann method is used to model a horizontal axis tidal turbine. Because tidal turbines generally operate in highly turbulent flows, a synthetic eddy method is implemented to generate realistic turbulent inflow condition. The approach makes use of the open-source code Palabos. Large eddy simulation is employed. A coupling between an immersed boundary method and a wall model is realized to model the turbine. Calculations are performed at two different turbulence rates. The upstream flow condition is first set up to match with experimental results. Numerical simulations of a tidal turbine with realistic turbulent inflow conditions are then realized with the lattice Boltzmann method. The approach is found to be in good agreement with experimental data. Cases with three different inflow turbulence rates are simulated. An almost linear evolution with the turbulence rate is observed for the axial velocity deficit. An analysis of the propagation of tip-vortices in the close wake is carried out. It is found that turbulence has a great impact on the tip-vortices propagation envelope.