This paper investigates the average consensus problem in directed networks of multi-agent systems with uncertain time-varying delays. Fixed and switching topologies that are kept weakly connected and balanced are firstly analyzed. The original system is then transformed into a reduced dimension model. Based on Jensen s inequality and reciprocally convex approach, sufficient conditions for average consensus are further presented. Specially, a less conservative upper bound of time-varying communication delays is derived in comparison with the existing results. Numerical examples confirm the effectiveness of the proposed method. This paper investigates the average consensus problem in directed networks of multi-agent systems with uncertain time-varying delays. Fixed and switching topologies that are kept weakly connected and balanced are reduced defined model. on Jensen s inequality and reciprocally convex approach, sufficient conditions for average consensus are further presented. Specially, a less conservative upper bound of time-varying communication delays is derived in comparison with the existing results.