The two-component Camassa-Holm equation includes many intriguing phenomena.We propose a multi-symplectic compact method to solve the two-component Camassa-Holm equation.Based on its multi-symplectic formulation,the proposed method is derived by the sixth-order compact finite difference method in spatial discretization and the symplectic implicit midpoint scheme in temporal discretization.Numerical experiments finely describe the velocity and density variables in the two-component integrable system and distinctly display the evolvement of the singular solutions.Moreover,the proposed method shows good conservative properties during long-time numerical simulation.