A matrix model with manifest ten-dimensional N=2 super Poincaré invariance is proposed, which is conjectured to be equivalent to superstring theory. The model is based on the large-N reduced model of ten-dimensional super Yang-Mills theory. The matrix model is shown to have the same massless spectrum as type IIB string theory, and its interactions between BPS-saturated states are analyzed. The model is related to the Green-Schwarz action of type IIB string theory in the Schild gauge. The matrix model is shown to have N=2 supersymmetry and Lorentz invariance. The one-loop effective action is calculated, and it is shown that the massless spectrum is consistent with that of type IIB string theory. The model is also shown to have a continuum limit that corresponds to the large-N reduced model of super Yang-Mills theory. The model is further shown to generate a chemical potential term, which is related to the eigenvalues of the gauge fields. The model is also shown to have a non-perturbative definition through the continuum limit of the large-N reduced model. The model is consistent with the N=2 supersymmetry and the cluster property of the theory. The parameters α and β are determined in terms of physical quantities, and the model is shown to be equivalent to the Nambu-Goto action of type IIB string theory. The model is also shown to have a double scaling limit, which is consistent with the large-N reduced model of super Yang-Mills theory. The model is further shown to have a one-loop renormalization, and the continuum limit is taken as the non-perturbative definition of the theory. The model is consistent with the N=2 supersymmetry and the cluster property of the theory. The model is shown to have a non-perturbative definition through the continuum limit of the large-N reduced model. The model is consistent with the N=2 supersymmetry and the cluster property of the theory.A matrix model with manifest ten-dimensional N=2 super Poincaré invariance is proposed, which is conjectured to be equivalent to superstring theory. The model is based on the large-N reduced model of ten-dimensional super Yang-Mills theory. The matrix model is shown to have the same massless spectrum as type IIB string theory, and its interactions between BPS-saturated states are analyzed. The model is related to the Green-Schwarz action of type IIB string theory in the Schild gauge. The matrix model is shown to have N=2 supersymmetry and Lorentz invariance. The one-loop effective action is calculated, and it is shown that the massless spectrum is consistent with that of type IIB string theory. The model is also shown to have a continuum limit that corresponds to the large-N reduced model of super Yang-Mills theory. The model is further shown to generate a chemical potential term, which is related to the eigenvalues of the gauge fields. The model is also shown to have a non-perturbative definition through the continuum limit of the large-N reduced model. The model is consistent with the N=2 supersymmetry and the cluster property of the theory. The parameters α and β are determined in terms of physical quantities, and the model is shown to be equivalent to the Nambu-Goto action of type IIB string theory. The model is also shown to have a double scaling limit, which is consistent with the large-N reduced model of super Yang-Mills theory. The model is further shown to have a one-loop renormalization, and the continuum limit is taken as the non-perturbative definition of the theory. The model is consistent with the N=2 supersymmetry and the cluster property of the theory. The model is shown to have a non-perturbative definition through the continuum limit of the large-N reduced model. The model is consistent with the N=2 supersymmetry and the cluster property of the theory.