In this paper, we find the necessary and sufficient condition for the simple, 2-connected, plane graphs to be isomorphic and the necessary and sufficient condition for the simple, connected, plane graphs to be isomorphic. And we find an algorithm to give all non-isomorphic embeddings of the simple, connected, planar graph by using this condition. Finally, we compute the numbers of the non-isomorphic embeddings of simple, connected, planar graphs and those of the simple, 2-connected, planar graphs with order p=8,9 and 10.