  In this paper, we study the non-self-dual extended Harper's model with a
Liouville frequency. Based on the work of \cite{SY}, we show that the
integrated density of states (IDS for short) of the model is
$\frac{1}{2}$-H$\ddot{\text{o}}$lder continuous. As an application, we also
obtain the Carleson homogeneity of the spectrum.
