In this paper we introduce a tree structured self-organizing network, called the Growing Hierarchical Tree SOM (GHTSOM), that combines unsupervised learning with a dynamic topology for hierarchical classification of unlabelled data sets. The main feature of the proposed model is a SOM-like self-organizing process that allows the network to adapt the topology of each layer of the hierarchy to the characteristics of the training set. In particular the self-organization is obtained in two steps: the first one concerns the learning phase and is finalized with the creation of a tree of SOMs, while the second one is in regard to the clustering phase and provides the formation of classes for each level of the tree (hence self-organization not only for training but also for the creation of topological connections). As a result the network works without the need for user-defined parameters. Experimental results are proposed on both synthetic and real data sets.