In this paper, a new robust routing formulation in a wireless mesh network (WMN) is proposed, which enables the routing strategy to be robust to random traffic fluctuation. Together with resource allocation in link layer, an optimization problem aiming at minimizing the total transmission power in the WMN is formulated and solved optimally. The research assumes only limited knowledge of the traffic distribution, in particular, arbitrary distribution with known mean and variance. Numerical results are presented to illustrate the features of the proposed strategy.