In this work, we proposed the hybrid non-convex regularizers for Poisson noise removal on medical images. The model is built by a combination of non-convex total variation and non-convex fractional total variation. The proposed model allows for avoiding the annoying staircase artifacts and obtaining the reconstruction results with sharp and neat edges during the noise removal process. For handling the minimization problem, we employ the alternating minimization method associated with the iteratively reweighted <i>l</i>₁ algorithm. Numerical experiments illustrate the efficiency of the proposed model and corresponding algorithm.