  Given a sequence $\{b_{i}\}_{i=1}^{n}$ and a ratio $\lambda \in (0,1),$ let
$E=\cup_{i=1}^n(\lambda E+b_i)$ be a homogeneous self-similar set. In this
paper, we study the existence and maximal length of arithmetic progressions in
$E$. Our main idea is from the multiple $\beta$-expansions.
