The restoration of blurred images corrupted by Poisson noise is an important task in various applications such as astronomical imaging, electronic microscopy, single particle emission computed tomography (SPECT) and positron emission tomography (PET). The problem has received significant attention in recent years. Total variation (TV) regularization, one of the standard regularization techniques in image restoration, is well known for recovering sharp edges of an image, but also for producing staircase artifacts. In order to remedy the shortcoming of TV in Poissonian image restoration, we consider a high-order total variation-based optimization model. The optimization model is converted to a constrained problem by variable splitting and then is addressed with the alternating direction method. Numerical results from the Poisson noise removal problem are given to illustrate the validity and efficiency of the proposed method.