  We present a renormalization group analysis for the hyperbolic sine-Gordon
(sinh-Gordon) model in two dimensions. We derive the renormalization group
equations based on the dimensional regularization method and the Wilson method.
The same equations are obtained using both these methods. We have two
parameters $\alpha$ and $\beta\equiv \sqrt{t}$ where $\alpha$ indicates the
strength of interaction of a real salar field and $t=\beta^2$ is related with
the normalization of the action. We show that $\alpha$ is renormalized to zero
in the high-energy region, that is, the sinh-Gordon theory is an asymptotically
free theory. We also show a non-renormalization property that the beta function
of $t$ vanishes in two dimensions.
