We present a systematic way for deriving a four-dimensional (4D) effective action of the five-dimensional (5D) orbifold supergravity respecting the N=1 {it off-shell} structure. As an illustrating example, we derive a 4D effective theory of the 5D gauged supergravity with a universal hypermultiplet and {it generic} gaugings, which includes the 5D heterotic M-theory and the supersymmetric Randall-Sundrum model as special limits of the gauging parameters. We show the vacuum structure of such model, especially the nature of moduli stabilization, introducing perturbative superpotential terms at the orbifold fixed points.
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