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This paper considers the multi-symplectic formulations of the generalized fifth-order KdV equation in Hamiltonian space.Recurring to the midpoint rule,it presents an implicit multi-symplectic scheme with discrete multi-symplectic conservation law to solve the partial differential equations which are derived from the generalized fifth-order KdV equation numerically.The results of the numerical experiments show that this multi-symplectie algorithm is good in accuracy and its long-time numerical behaviour is also perfect.