  Let $X$ be a smooth complex projective curve, and let $x\in X$ be a point. We
compute the automorphism group of the moduli space of framed vector bundles on
$X$ of rank $r \geq 2$ with a framing over $x$. It is shown that this
automorphism group is generated by the following three: (1) pullbacks using
automorphisms of the curve $X$ that fix the marked point $x$, (2) tensorization
with certain line bundles over $X$ and (3) the action of
$\operatorname{PGL}_r(\mathbb{C})$ through composition with the framing.
