The role of zonal flows in the formation of transport barrier in helical plasmas is analysed using the transport code. A set of one-dimensional transport equations is analysed, including the effect of zonal flows. The turbulent transport coefficient is shown to be suppressed when the plasma state takes the strong positive radial electric field. This bifurcation of the turbulent transport is newly caused by the change of the damping rate of zonal flows. It is theoretically demonstrated that the damping rate of zonal flows plays an important role in global confinement in toroidal plasmas.