Cupping artifact is one of the most serious problems in a middle-low energy X-ray Flat panel detector (FPD)-based cone beam CT system. Both beam hardening effects and scatter could induce cupping artifacts in reconstructions and degrade image quality. In this paper, a two-step cupping-correction method is proposed to eliminate cupping: 1) scatter removal; 2) beam hardening correction. By experimental measurement using Beam Stop Array (BSA), the X-ray scatter distribution of a specific object is estimated in the projection image. After interpolation and subtraction, the primary intensity of the projection image is computed. The scatter distribution can also be obtained using convolution with a low-pass filter as kernel. The linearization is used as beam hardening correction method for one-material object. For two-material cylindrical objects, a new approach without iteration involved is present. There are three processes in this approach. Firstly, correct raw projections by the mapping function of the outer material. Secondly, reconstruct the cross-section image from the modified projections. Finally, scale the image by a simple weighting function. After scatter removal and beam hardening correction, the cupping artifacts are well removed, and the contrast of the reconstructed image is remarkably improved.