Explosive data traffic growth has led to a continuous surge in capacity demands in mobile networks. In order to provision high network capacity, small cell base stations (SCBSs) are widely deployed. Owing to the close proximity to mobile users, SCBSs can effectively enhance the network capacity and offloading traffic load from macro BSs (MBSs). However, the cost-effective backhaul may not be readily available for SCBSs that leads to backhaul constraints in small cell networks. In this paper, we investigate the traffic offloading in backhaul constrained small cell networks. We have proposed a network latency aware user association scheme that balances traffic loads among base stations (BSs) to minimize the average traffic delivery latency of the mobile network. The proposed network latency aware user association scheme considers the traffic delivery latency in both BSs and their backhaul during the process of establishing user associations. We have proved that the proposed user association scheme converges to the optimal solution that minimizes the average traffic delivery latency of the network. The simulation results show that the proposed scheme reduces the average traffic delivery latency by 63% and 34% as compared to the user association scheme that considers only the traffic delivery latency in BSs and a two-tier data rate bias user association scheme, respectively.