In this paper,we propose a local conservation law for the Zakharov system.The property is held in any local timespace region which is independent of the boundary condition and more essential than the global energy conservation law.Based on the rule that the numerical methods should preserve the intrinsic properties as much as possible,we propose a local energy-preserving (LEP) scheme for the system.The merit of the proposed scheme is that the local energy conservation law can be conserved exactly in any time-space region.With homogeneous Dirchlet boundary conditions,the proposed LEP scheme also possesses the discrete global mass and energy conservation laws.The theoretical properties are verified by numerical results.