For simulating incompressible two-phase fluid flows, several phase-field lattice Boltzmann (LB) methods based on the local Allen-Cahn (AC) equation have been intensively proposed in recent years. We present a local hybrid AC model for the phase-field LB method. In the proposed model, the local and nonlocal AC equations are linearly combined using a local weight assigned in the interface or bulk phase regions individually. Five numerical problems, namely diagonal translation, Zalesak's disk rotation, static bubble, two bubbles of different radii, and Rayleigh-Taylor instability, are simulated for validation. The numerical results agree well with the analytical solutions or available previous results. Additionally, the numerical dispersion and the coarsening phenomenon are considerably suppressed in the proposed model. Finally, the performance of the proposed model is validated by conducting a drainage simulation in porous media and compared with the global hybrid AC model.