This paper introduces the simulation method of concrete temperature cracking propagation process by element-free Galerkin method (EFGM). Due to its no-remeshing property, EFGM is very suitable for cracking problem. The governing equation of EFGM is presented for concrete heat conduction problem. A numerical simulating program is developed and an example including an initial crack is computed to validate the program. Result shows good accuracy and reliability of this method and cracking process may be simulated effectively by EFGM.