Improving the solving performance of large-scale security constrained economic dispatching optimization model is the premise and foundation of carrying out the global optimization and balance of large-scale power grid. The physical characteristics of the safety constrained economic dispatch problem are first analyzed, and the time-varying constrained relaxation model without considering the unit climbing constraints is solved by parallel computation. Based on the analysis of relaxation solutions, useful information for guiding the improvement of security constrained economic dispatch model is obtained. A fast solution method of large-scale security constrained economic dispatch based on heuristic linear programming is proposed by eliminating constraints and increasing constraints. The proposed algorithm is applied to the new England 10 machine expansion system and the actual power grid in China, and the accuracy and effectiveness of the algorithm is verified. This work is supported by Science and Technology Project of the Headquarter of State Grid Corporation of China (No. 5442DZ180019) and Innovation Fund of China Electric Power Research Institute (No. 5242001700G3).