This paper investigates the degree of congestion and efficiency in complex traffic networks, by introducing congestion effects, which can be described by flow-based link cost functions. Different network topologies including random networks, small-world networks and scale-free networks are explored. The impact of different distributions of capacity and origin-destination traffic demand on the degree of congestion and efficiency in complex networks is mainly studied. A phase transition from free flow state to traffic jams can be uncovered. The relationship between congestion and efficiency in complex networks is also discussed.