We prove that the Schützenberger graph of any element of the HNN-extension of a finite inverse semigroup $S$ with respect to its standard presentation is a context-free graph in the sense of [11], showing that the language $L$ recognized by this automaton is context-free. Finally we explicitly construct the grammar generating $L$, and from this fact we show that the word problem for an HNN-extension of a finite inverse semigroup $S$ is decidable and lies in the complexity class of polynomial time problems.