Abstract: Discusses a class of problems on complex network traffic that has a fixed bandwidth, and develops a relevant model with link bandwidth constraint. Taking the information flow in traffic as a background, the change in network load with different bandwidth constraints is investigated qualitatively in a BA scale-free network with an "adjustable clustering coefficient". It is found that there is a high load capacity in the network with wide bandwidth, and the load capacity in the network is reduced greatly with reinforcing bandwidth constraint. When the bandwidth constraint is reinforced to its permissible limit, the load capacity of network traffic has already not been affected by the capacity of data processing package. The reason why the bandwidth constraint affects network traffic is analyzed qualitatively from the perspective of complex network topology and traffic mechanism.