If traffic is congested in a network, the authorities always try to relieve the congestion by transportation system management methods (TSM) first. However, the effects of TSM are restricted by the capacity of the network. The main solution of congestion in long term transportation system planning is to increase road capacity appropriately. Braess (1968) discovered that as a new road link is added on a network and after reaching its user equilibrium, each user's travel time may increase. Thus, increasing a new link may not only make the congestion more serious, but also waste the construction budget and time. Researchers devoted to discuss the sufficient and necessary condition so as to prevent the occurrence of paradox. Pas (1997) mentioned that ifthe road price is charged as marginal cost, the paradox will disappear. In spite of the paradox seems to be solved, the discussion was under certain travel demand condition. In practice, travel demand will change during the planning and construction period and may also change with travel cost. The propose of this paper is going to discuss Braess' paradox under variant demand, and use the classical Braess' network as an example to explain it.