  Wolf gave a homeomorphism from the Teichm\"uller space to the space of
quadratic differentials on a closed Riemann surface by using harmonic maps.
Moreover, using harmonic maps rays, he gave a compactification of the
Teichm\"uller space and show that it coincides with the Thurston
compactification. In this paper, we extend the harmonic maps compactification
to the Teichm\"uller spaces of punctured Riemann surfaces, and show that it
still coincides with the Thurston compactification.
