In this paper, a new network structure called generalized Hierarchical Completely-Connected networks (HCC) is proposed, and its properties and features are evaluated. A set of the HCCs constructed by the proposed method includes some conventional hierarchical networks, then it is called generalized one. The construction of an HCC is started from a basic block (a level-$1$ block) which consists of $n$ nodes with a constant degree. Then a level-$h$ ($h \geq 2$) block is constructed recursively by interconnecting any pair of macro nodes ($n$ level-($h-1$) blocks) completely. An HCC has the constant node degree regardless of increasing its size (the number of nodes). Furthermore, since an HCC has the hierarchically structured character and the feature of uniformity, a wide variety of inter-cluster connections are possible.