Image reconstruction algorithms implemented in existing computed tomography (CT) scanners require that the projection data should be available in proportional-space. The image reconstruction from the projections viewed from few angles has already been one of the hot problems in the research of iterative reconstruction algorithms. Total variation (TV)-based CT image reconstruction has shown to be experimentally capable of producing accurate reconstructions from sparse-view data. Reconstruction algorithms based on alternating direction method (ADM) show higher performance among these TV-based algorithms. However, computing the pseudoinverse at each iteration is too costly to implement numerically in the exact ADM algorithm. For this problem, then inexact ADM is adopted, which uses linearization and proximal points techniques such that computing the pseudoinverse can be accomplished by fast Fourier transforms. Experimental results demonstrate that the proposed method can accelerate the exact ADM algorithm, with little accuracy loss, and the computing time is approximatively reduced by 30%.