Total variation(TV) minimization model has been widely used in the field of image reconstruction. It can achieve accurate reconstruction under sparse projection acquisition by minimizing L1 norm of first-order image gradient size transformation. However, the TV model is based on the assumption of segmented smooth image, which sometimes leads to staircase effect. Researches show that the high-order Total Variation(HOTV) model can suppress the staircase effect effectively and improve the reconstruction accuracy. In addition, total p-variation(TpV, 0 < p
≤ 1) model uses Lpnorm to approximate L0 norm, which is expected to further improve the sparse reconstruction ability. In view of this, this paper combines HOTV model with TpV model, a new high-order TpV(HOTpV) reconstruction model is proposed, which is solved by adaptive steepest descent-projection onto convex sets(ASD-POCS) algorithm, sparse reconstruction experiments are carried out on grayscale gradual simulation phantom and real CT image simulation phantom under ideal and noisy conditions. The experimental results show that compared with TV, TpV and HOTV, HOTpV can get the highest accuracy image.