Network transport is an important aspect of geographical information science, transportation, complex networks, etc. Previous studies have shown that the transport capacity of street networks can be enhanced by improving routing algorithms. However, the upper throughput limit of street networks is unknown in detail. This article studies the transport process of networks and finds that any connected network has a maximum throughput depending on the topological and structural properties of the network. Based on this, the maximum throughput of street networks is obtained. Experiments show that when the street network remains unchanged, the maximum throughput of the street network is limited and is dependent on road capacity and average path length, regardless of adopted routing algorithms. Our findings suggest that the throughput of networks can be improved by increasing node capacity or decreasing average path length, but the maximum transport capacity of the network cannot be greater than the ratio of the sum of all the nodes' capacities to the average path length of the network, no matter what routing strategies are adopted. This study is expected to be a starting point for more sophisticated research in network transport, such as evaluating the inherent throughput of an urban street network.