In communication networks (CNs), the uncertainty is caused by the dynamic nature of the traffic demands. Therefore there is a need to incorporate the uncertainty into the network bandwidth capacity design. For this purpose, this paper developed a fuzzy methodology for network bandwidth design under demand uncertainty. This methodology is usually used for offline traffic engineering optimization, which takes a centralized view of bandwidth design, resource utilization, and performance evaluation. In this proposed methodology, uncertain traffic demands are first handled into a fuzzy number via a fuzzification method. Then a fuzzy optimization model for the network bandwidth allocation problem is formulated with the consideration of the trade-off between resource utilization and network performance. Accordingly, the optimal network bandwidth capacity can be obtained by maximizing network revenue in CNs. Finally, an illustrative numerical example is presented for the purpose of verification.