Abstract: FBP is the most popular analytical algorithm used to reconstruct image in CT system.The filtering process before back projection plays an important role relate to the image reconstruction quality.Usually the filtering function is acquired by Ramp function multiplying a rectangular window;however the ideal rectangular window will lead to a rough reconstruction result because of Gibbs artifact.According to the theory of infinite series,the arithmetic average named Fejer-core can be abstained after the function is expanded to the form of part sum.The core function has superiority convergence property.So to avoid Gibbs phenomena,the paper advances an improvement filtering method.Experiment result shows that Gibbs is avoided when convolve the filtered projections with Fejer-core.So smooth image can be obtained.