  In this paper, we first obtain the sub-Laplacian comparison theorem in a
complete noncompact pseudohermitian manifold of vanishing torsion (i.e.
Sasakian manifold). Secondly, we derive the sub-gradient estimate for positive
pseudoharmonic functions in a complete noncompact pseudohermitian manifold
which satisfies the CR sub-Laplacian comparison property. It is served as the
CR analog of Yau's gradient estimate. As a consequence, we have the natural CR
analogue of Liouville-type theorems in a complete noncompact Sasakian manifold
of nonnegative pseudohermitian Ricci curvature tensors.
