Effective assessment of the importance of grid lines and nodes is of great significance for building the core backbone grid.The fuzzy theory is introduced into risk assessment with fuzzy numbers used to describe the uncertainties of generator and load.A new method for assessing the importance of lines is put forward and，by referring to the importance of node proximity and node criticality the importance of nodes is obtained.Furthermore，a model for building the core backbone grid considering the importance of lines and nodes is developed.The discrete particle swarm optimization algorithm is used to search for the backbone grid.Simulation examples demonstrate that the proposed method can effectively solve the problem of assessing the importance of lines and nodes in the grid.The backbone grid construction scheme obtained can not only guarantee normal power supply of important load，but also selectively retain important components while minimizing nodes and lines.