It is a fundamental problem to construct a virtual path layout minimizing the hop number as a function of the congestion for a communication network. It is known that we can construct a virtual path layout with asymptotically optimal hop number for a mesh of trees network, butterfly network, cube-connected-cycles network, de Bruijn network, shuffle-exchange network, and complete binary tree network. The paper shows a virtual path layout with minimum hop number for a complete binary tree network. A generalization to complete k-ary tree networks is also mentioned.