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An outerplanar graph is a planar graph which can be embedded in the plane in such a way that all of vertices lie on the outer boundary. Many chemical compounds are known to be expressed by outerplanar graphs. In this paper, firstly, we introduce an externally extensible outerplanar graph pattern (eeo-graph pattern for short) as a graph pattern common to a finite set of outerplanar graphs like a dataset of chemical compounds. The eeo-graph pattern can express a substructure common to blocks which appear in outerplanar graph structured data. Secondly, we propose a data mining algorithm for enumerating all maximal frequent eeo-graph patterns from a finite set of outerplanar graphs. Finally, we report experimental results on a chemical dataset.