The $n$-$book ~embedding$ of a graph $G$ is an embedding of the graph $G$ in an $n$-book with the vertices of $G$ on the spine and each edge to the pages without crossing each other. If the degree of vertices of $G$ at most one in each page, the $n$-book embedding is $matching$. The $matching~ book~ thickness$ of graph $G$ is the smallest $n$ so that $G$ can be matching embedded in an $n$-book. In this paper, the matching book thickness of the biconnected outerplanar graphs is determined.