  We construct a D3-brane wrapped on S^1, which is fibred over the resolved
conifold as its transverse space. Whereas a fractional D3-brane on the resolved
conifold is not supersymmetric and has a naked singularity, our solution is
supersymmetric and regular everywhere. We also consider an $S^1$-wrapped
D3-brane on the resolved cone over T^{1,1}/Z_2, as well as on the deformed
conifold. In the former case, we obtain a regular supergravity dual to a
certain four-dimensional field theory whose Lorentz and conformal symmetries
are broken in the IR region and restored in the UV limit.
