The exterior computed tomography (CT) problem is one kind of truncation problem. It is very ill-posed, so that accurate reconstruction of the attenuation function is hardly possible from real data. Based on projection onto convex sets (POCS) algorithm, total variation minimization (TVM) methods, and C-V model, we develop and investigate a new iterative reconstruction algorithm, which is referred to as subregion-averaged-TVM-POCS (SA-TVM-POCS). Numerical simulations are presented to illustrate the efficiency of the algorithm. The results of this paper can be easily applied to other x-ray CT reconstruction problems.