A phase-field-based lattice Boltzmann model is proposed for the interface capturing of multi-phase flows based on the conservative Allen-Cahn equation (ACE).By adopting the improved form of a relaxation matrix and an equilibrium distri-bution function,the time derivative (e)t (φu) induced by recovering the diffusion term in ACE is eliminated.The conducted Chapman-Enskog analysis demonstrates that the correct conservative ACE is recovered.Four benchmark cases includ-ing Zalesak\'s disk rotation,vortex droplet,droplet impact on thin film,and Rayleigh-Taylor instability are investigated to validate the proposed model.The numerical results indicate that the proposed model can accurately describe the complex interface deformation.