It is a core task to find solutions to suppress the "shuttle effect" of polysulfides and improve high rate capability at the sulfur cathode of lithium sulfur batteries. Herein we first time propose a concept of multileveled blocking "dams" to suppress the diffusion of polysulfides. We report a facile and effective strategy to construct multidimensional conductive carbon hosts for accommodation of active sulfur. Multidimensional ternary carbon networks (MTCNs) with OD nanospheres, 1D nanotubes and 2D nanoflakes are organically combined together to provide multileveled conductive channels to reserve active sulfur and promote stable sustained reactions. In the light of enhanced conductivity and multi leveled blocking "dams" for polysulfides, the designed MTCN5/S cathode has been demonstrated with noticeable improvement in discharge capacity (1472 mAh g(-1) at 0.1 C) and long-term cycling stability (65% retention at 5.0 C after 500 cycles). Our research may provide a new insight in the gradient blocking of polysulfides with the help of multidimensional carbon networks. (C) 2016 Elsevier B.V. All rights reserved.