Abstract: We focus on the new kind of P-stable Obrechkoff method for the numerical solution of orbital problemsHowever, only a few of these differential equations can be solved exactlyApproximate methods are the main means for solving, analyzing and understanding physics problemsThrough improving the Wangs method, we develop a new kind of P-stable four-step Obrechkoff method by adding the higher-order derivativesThis proposed method is very effective but has very high local truncation errorThe numerical experiments for the numerical solution of orbital problems has the advantage over the Wangs method in accuracy and efficiency