This paper focuses on dealing with the nonlinearities in network congestion control. The nonlinearities are reflected in time-varying perturbations in the state and delayed state with unknown bounding coefficients, which have not been considered in the existing congestion control methods. A new system model is established for networks with unmatched nonlinearities, uncertainties and time-varying delays, and a new state feedback congestion controller is designed based on adaptive control. Finally, the stability and the performance of the closed-loop system are validated via a new Lyapunov-Krasovskii functional and linear matrix inequality. The effectiveness and feasibility of the proposed congestion controller are verified through simulations.