Abstract: In order to enrich the theory of the Dirichlet space, the mathematical structure of the multiplier algebra of Dirichlet space is studied by applying concepts of inner function and outer function. At first, the inclusion relations between multiplier algebra, intersection set algebra and D_α algebra of Dirichlet space is given and then properties of their inner function and outer function is investigated. Finally, the quotient decomposition theory of outer function in multiplier algebra of Dirichlet space was obtained.