  In this paper we apply the entropy function formalism to the two-dimensional
black hole which come from the compactification of the heterotic string theory
with the dilaton coupling function. We find the Bekenstein-Hawking entropy from
the value of the entropy function at its saddle point. Also we consider higher
derivative terms. After that we apply the entropy function formalism to the
Jackiw-Teitelboim (JT) model where we consider the effect of string-loop to
this model.
