Abstract. We construct a large-N twisted reduced model of the four-dimensional super Yang-Mills theory coupled to one adjoint matter. We first consider a non-commutative version of the four-dimensional superspace, and then give a mapping rule between matrices and functions on this space explicitly. Our reduced model is compared with the Dijkgraaf-Vafa theory that claims the low-energy glueball superpotential of the original gauge theory is governed by a simple one-matrix model. We show that their claim can be regarded as the large-N reduction in the sense that the one-matrix model they proposed can be identified with our reduced model. The map between matrices and functions enables us to make direct identities between the correlators of the gauge theory and the matrix model. As a by-product, we can give a natural explanation for the unconventional treatment of the onematrix model in the Dijkgraaf-Vafa theory where eigenvalues lie around the top of the potential.

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