In this paper, a mass conservative lattice Boltzmann model (LBM) is proposed to simulate the two-phase flows with moving contact lines at high density ratio. The proposed model consists of a phase field lattice Boltzmann equation (LBE) for solving the conservative Allen-Cahn (A-C) equation, and a pressure evolution LBE for solving the incompressible Navier-Stokes equations. In addition, a modified wall boundary treatment scheme is developed to ensure the mass conservation. The wetting dynamics are treated by incorporating the cubic wall energy in the expression of the total free energy. The current model is characterized by mass conservation, proper treatment of wetting boundary and high density ratio. We applied the model on a series of numerical tests including equilibrium droplets on wetting surfaces, co-current flow and a droplet moving by gravity along inclined wetting surfaces. Theoretical analysis and experiments were conducted for model validation. The numerical results show good performances on mass conservation even with a density contrast up to 1000. Furthermore, the results show that the moving contact line can be successfully recovered, which proves that this model is applicable on the study of moving contact line issue and further related applications.