Recently, network operators are confronting the challenge of exploding traffic and more complex network environments due to the increasing number of access terminals having various requirements for delay and package loss rate. However, traditional routing methods based on the maximum or minimum single metric value aim at improving the network quality of only one aspect, which makes them become incapable to deal with the increasingly complicated network traffic. Considering the improvement of deep learning techniques in recent years, in this paper, we propose a smart packet routing strategy with Tensor-based Deep Belief Architectures (TDBAs) that considers multiple parameters of network traffic. For better modeling the data in TDBAs, we use the tensors to represent the units in every layer as well as the weights and biases. The proposed TDBAs can be trained to predict the whole paths for every edge router. Simulation results demonstrate that our proposal outperforms the conventional Open Shortest Path First (OSPF) protocol in terms of overall packet loss rate and average delay per hop.