Abstract: Treanor's explicit method is typical among the numerical integrators for ODEs . There is yet some problems when used to cope with stiff equations . In this paper , the stability characteristics of Treanor's method are analyzed and discussed.By using Richardson extrapolation, an improved method based on Treanor's method the Treanor-Richar-dosn predict or-correct or method is suggested . Analysis and numerical computation have made it-clear that the,new method has greater stability region than the Treanor's method and the accuracy of the numerical solution can be increased as compared with that of the Treanor's method . T- R method is more suitable for integration of stiff ODEs . It is a better numerical solver in digital simulations .