Summary: The zero-temperature phase transition of the one-dimensional Bose-Hubbard model with nearest-neighbor interaction is investigated by using the finite size density matrix renormalization group method (FS-DMRG). By calculating the energy and associated eigenstate of the system’s ground state with certain parameters, the local density, chemical potential and the compressibility are obtained, from which different phases, i. e. superfluid (SF), Mott insulator (MI) and the charge density wave (CDW), can be characterized. In addition, from the phase diagram, the critical conditions of transitions are gotten from MI to SF and CDW to SF. All these results obtained are more accurate than those of previous researches.