Summary: The max-plus algebra is a semiring on \(\mathbb{R}_{\max}=\mathbb{R}\cup\{-\infty\}\) with addition \(\oplus\) and multiplication \(\otimes\) defined by \(\oplus=\max\) and \(\otimes=+\), respectively. It is known that eigenvalues of max-plus matrices are equivalent to the maximal average weight of the corresponding directed graph. In [S. Watanabe et al., Linear Algebra Appl. 598, 29–48 (2020; Zbl 1437.05152)], authors introduced the max-plus walk which is a walk model on one dimensional lattice on \(\mathbb{Z}\) over max-plus algebra, and discussed its properties such as the conserved quantities and the steady state. In this paper, we will discuss the limit measure of the max-plus walk.