This paper presents a correcting method for classical f and g series which is to be used in cases considering the primary perturbations of the zonal harmonics. It overcomes the limitation of f and g series only suitable to short arc. The results derived with CA system REDUCE are also given. Comparing the results using this corrected f and g series with those from direct numerical integration method，we can see that the former is faster and with the same accuracy. Besides，it can provide continuous states instead of discrete ones. Its clarity and effectiveness make it very useful in space engineering.