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Based on the full wave simulation and the Maxwell stress tensor theory, we demonstrate an enhanced transverse optical gradient force acting on Rayleigh particles immersed in a simple optical field formed by two linearly polarized plane waves. The optical gradient force acting on a conventional dielectric particle can be enhanced by two orders of magnitude via coating an extremely thin silver shell, whose thickness is only about one-tenth of the dielectric core. The analytical results based on the multipole expansion theory reveal that the enhanced optical gradient force comes mostly from the interaction between the incident field and the electric quadrupole excited in the core-shell particle. It is worth noting that the force expression within the dipole approximation commonly used for Rayleigh particles is invalid in our situation, even the particle is within the Rayleigh regime. In addition, both the optical potential energy and the optical trapping stiffness for the core-shell particle exhibit a great enhancement by two orders of magnitude stronger than a conventional dielectric particle and thus is favorable to a stable optical trapping. These results may extend the application range of optical tweezers and enrich optical manipulation techniques.