On the category of modules of Gorenstein dimension zero II

Let R be a commutative noetherian henselian non-Gorenstein local ring. The author has conjectured in [R. Takahashi, On the category of modules of Gorenstein dimension zero, preprint, 2003] that there exist infinitely many isomorphism classes of indecomposable R-modules of Gorenstein dimension zero if there exists a non-free module of Gorenstein dimension zero, and has proved that the conjecture holds when R has depth zero. In this paper, we prove that the conjecture also holds when R has depth one.