The Chambolle-Pock (CP) algorithm has been successfully applied for solving optimization problems involving various data fidelity and regularization terms. However, when applied to CT image reconstruction, its efficiency is still far from being satisfactory. Another problem is that unmatched forward and backward operators are commonly used for CT reconstruction, in which case, the CP algorithm might fail to converge well. In this paper, based on a operator-splitting perspective of the simultaneous algebraic reconstruction technique (SART), the CP algorithm is generalized to incorporate the ordered subsets technique for fast convergence. The energy functional associated with the optimization problem is split into multiple terms, and the CP algorithm is employed to minimize each of them in an iterative manner. Numerical experiments show that the proposed algorithm could gain more than ten times faster convergence speed compared to the classical CP algorithm.