Supersymmetric formulation of a spinning particle interacting with external gauge fields is investigated based on the high-dimensional unification of the gravitational field and non-Abelian gauge fields. It is shown that, associated with the dimensional reduction from the (4+ N) dimensional spacetime to the 4-dimensional spacetime and an extra N-dimensional (compact) space, the metric tensor in the extra subspace is absorbed into the mass term of the particle and generates discrete spectrum. Recently, the high-dimensional unified theori),2),3) has renewedly attracted interest as a possible framework including the unified gauge theory of weak and electromagnetic interactions of the Weinberg-Salam type) In such a theory, one firstly sets up a geometry in (4 + N )-dimensional spacetime and then reduces the spacetime into the usual 4-dimensional spacetime and an extra N-dimensional space. In the reduced 4-dimensional theory, there arise the gravitational field, non-Abelian gauge fields and Higgs like scalar fields associated with the com ponents of the metric tensor gaP, gai and gij respectively. Here, Greek and Latin letters represent each vector index in the usual spacetime and the extra space. Furthermore, a simple particle in the (4 + N )-dimensional spacetime acquires, after the dimensional reduction, an internal structure as a particle in the usual 4-dimensional spacetime_ In this case, it will be necessary to assume the com pactness of the extra space in order to get discrete mass spectra from such an internal structure of the particle. In the high-dimensional unified theory, however, there are various viewpoints on the Higgs like scalar fields. For example, in the 5-dimensional theory of Kaluza and Klein,I) the freedom of such a scalar field was discarded. Scherk and Schwarz 3 ) investigated the possibility of occurring the symmetry breaking of non Abelian gauge fields due to the presence of Higgs like scalar fields and showed the instability of vacuum provided that the symmetry group of the extra space is semi simple. Thus, in the high-dimensional unified theory, the role of Higgs like scalar fields is not yet decisive. In the present paper, we investigate a supersymmetric formulation of the