  Noisy teleportation of nonclassical quantum states via a two-mode
squeezed-vacuum state is studied with the completely positive map and the
Glauber-Sudarshan $P$-function. Using the nonclassical depth as a measure of
transmission performance, we compare the teleportation scheme with the direct
transmission through a noisy channel. The noise model is based on the coupling
to the vacuum field. It is shown that the teleportation channel has better
transmission performance than the direct transmission channel in a certain
region. The bounds for such region and for obtaining the nonvanished
nonclassicality of the teleported quantum states are also discussed. Our model
shows a reasonable agreement with the observed teleportation fidelity in the
experiment by Furusawa et al. [Science {\bf 282}, 706 (1998)]. We finally
mention the required conditions for transmitting nonclassical features in real
experiments.
