A plane graph is a drawing of a planar graph in the plane
such that no two edges cross each other.
A rooted plane graph has a designated outer vertex.
For given positive integers $n\geq 1$ and $g\geq 3$,
let ${\cal G}_3(n,g)$ denote the set of
all triconnected rooted plane graphs with exactly
$n$ vertices such that the size of each inner face
is at most $g$.
In this paper, we give an algorithm that enumerates
all plane graphs in ${\cal G}_3(n,g)$.
The algorithm runs in constant time per each by outputting
the difference from the previous output.