Cone-beam X-ray luminescence computed tomography (CB-XLCT) imaging is a new medical imaging technique that can effectively detect early tumors in vitro. Sparse-view CB-XLCT imaging brings this technology a step closer to real-time imaging of CB-XLCT technique. Nevertheless, it suffers from a much more severe ill-conditioned inverse problem compared with traditional multi-view imaging, which poses a challenge to the extension of the traditional approach. A sparse non-convex L_p (0<p<1) model was employed to formulate an iteratively reweighted splitting augmented Lagrangian shrinkage algorithm. The classic non-convex operator was then combined with the algorithm to design a robust and steady method of extracting permissible regions so that it could guide the accurate reconstruction of the target as optimized prior knowledge. Digital rat and physical phantom experiments were designed and combined respectively with the classic representative algorithms of the L₁-norm and L₀-norm to evaluate the efficiency and robustness of the proposed method. The experimental results demonstrate that our proposed method can effectively solve the inverse problem of sparse-view CB-XLCT imaging and possesses expandability.