  In this paper, we study how to draw Halin-graphs, i.e., planar graphs that
consist of a tree $T$ and a cycle among the leaves of that tree. Based on
tree-drawing algorithms and the pathwidth $ pw(T) $, a well-known graph
parameter, we find poly-line drawings of height at most $6pw(T)+3\in O(\log
n)$. We also give an algorithm for straight-line drawings, and achieve height
at most $12pw(T)+1$ for Halin-graphs, and smaller if the Halin-graph is cubic.
We show that the height achieved by our algorithms is optimal in the worst case
(i.e. for some Halin-graphs).
