X-ray scatter poses a significant limitation to image quality in cone-beam CT (CBCT), as well as beam hardening, resulting in image artifacts, contrast reduction, and lack of CT number accuracy. Meanwhile the x-ray radiation dose is also non-ignorable. Considerable scatter or beam hardening correction methods have been developed, independently, and rarely combined with low-dose CT reconstruction. In this paper, we combine scatter suppression with beam hardening correction for sparse-view CT reconstruction to improve CT image quality and reduce CT radiation. Firstly, scatter was measured, estimated, and removed using measurement-based methods, assuming that signal in the lead blocker shadow is only attributable to x-ray scatter. Secondly, beam hardening was modeled by estimating an equivalent attenuation coefficient at the effective energy, which was integrated into the forward projector of the algebraic reconstruction technique (ART). Finally, the compressed sensing (CS) iterative reconstruction is carried out for sparse-view CT reconstruction to reduce the CT radiation. Preliminary Monte Carlo simulated experiments indicate that with only about 25% of conventional dose, our method reduces the magnitude of cupping artifact by a factor of 6.1, increases the contrast by a factor of 1.4 and the CNR by a factor of 15. The proposed method could provide good reconstructed image from a few view projections, with effective suppression of artifacts caused by scatter and beam hardening, as well as reducing the radiation dose. With this proposed framework and modeling, it may provide a new way for low-dose CT imaging.