A new reconstruction algorithm is introduced to obtain a high quality computerized tomography image from limited information. There are many practical cases in which only limited projection data can be collected due to the physical constraints of the hardware system and the object structure. In these cases, conventional reconstruction algorithms which require complete projections are often unacceptable because it causes severe streak artifacts and distortions. So image reconstruction from limited information is very important and many authors have contributed to it. But the methods presented are often time consuming, less efficient and some algorithm's convergency cannot be guaranteed. For iterative algorithms, it is more important to guarantee the convergency and accelerate the convergency speed. In this paper, a CT image reconstruction method which exploits the Helgason-Ludwig consistency condition is designed to consider obtainable information content about object and reconstruction error in the situation of a finite number of projections. Based on the consideration, we developed a new iterative algorithm which can reconstruct high quality artifactless CT image from limited information, and we design a new histogram constraint obtained from a priori knowledge to guarantee the convergency and to acquire high convergency speed. The results of simulated tests show the great advantages of this new method.