Enhancement effect of surface plasmon in the metal nano-particle is a hot topic in nano-material field. A system is investigated where a spherical metal nano-particle is placed near a dye molecule. Under the optical excitation of a polarized electric field the subsequent charge transfer dynamics for different relative positions are simulated by density matrix theory approach, where the Coulomb interaction of molecule and metal nano-particle is calculated in the framework of the dipole-dipole approximation. It is found that the enhancement effect is closely related to the relative distance between the molecule and metal nano-particle. Effect of enhancement due to the surface plasmon is discussed in detail for various coupling interactions, polarization of field, lifetime of plasmon, and non-resonant excitation; and the physical essence in the molecule-metal nano-particle coupled system is analysed.