Frequent closed pattern discovery is one of the most important topics in the studies of the compact representation for data mining. In this paper, we consider the frequent closed pattern discovery problem for a class of structured data, called attribute trees (AT), which is a subclass of labeled ordered trees and can be also regarded as a fragment of description logic with functional roles only. We present an efficient algorithm for discovering all frequent closed patterns appearing in a given collection of attribute trees. By using a new enumeration method, called the prefix-preserving closure extension, which enable efficient depth-first search over all closed patterns without duplicates, we show that this algorithm works in polynomial time both in the total size of the input database and the number of output trees generated by the algorithm. To our knowledge, this is one of the first result for output-sensitive algorithms for frequent closed substructure disocvery from trees and graphs.