Tree Adjoining Grammar (TAG) is a useful grammatical tool to model RNA secondary structures containing pseudoknots, but its time complexity for parsing is not small enough for the practical use. Recently, Weinberg and Ruzzo proposed a method of approximating stochastic context free grammar by stochastic regular grammar and applied it to faster genome annotation of non-coding RNA families. This paper proposes a method for extending their idea to stochastic approximation of TAGs by regular grammars. We will also report some preliminary experimental results on how well we can filter out non candidate parts of genome sequences by using obtained approximate regular grammars.