  Let $(X, A)$ be a nonsingular polarized toric 3-fold. We show that if the
adjoint bundle of $A$ has no glabal section, then all ample line bundles on $X$
are normally generated. Even if the adjoint bundle is effective, if it is not
big, then it is shown the normal generation. In particular, we show that all
ample line bundles on a nonsingular toric Fano 3-fold are normally generated.
