  We consider co-rotational wave maps from the $(1+d)$-dimensional Minkowski
space into the $d$-sphere for $d\geq 3$ odd. This is an energy-supercritical
model which is known to exhibit finite-time blowup via self-similar solutions.
Based on a method developed by the second author and Sch\"orkhuber, we prove
the asymptotic nonlinear stability of the "ground-state" self-similar solution.
