When serious fault happens, one of the main tasks of grid self-healing function is to avoid voltage instability effectively. For the power system with serious fault, this paper divides the process of voltage self-healing into two steps: recovering system stability and enhancing node voltage according to system stability and voltage amplitude. Then for each step, based on graph theory, the load which will be cut is determined according to the power flow before fault and the power flow after fault respectively. Then load is cut off successively using dichotomy until the system recovers voltage stability and maintains system voltage meeting a certain level. The simulation results of IEEE 30-bus system and a regional 17-bus system show that the method is simple and effective.