The sparse vector solutions for an underdetermined system of linear equations Ax = b have many applications in signal recovery and image reconstruction in tomography. Under certain conditions, the sparsest solution can be found by solving a constrained l₁ minimization problem: min ||x||₁ subject to Ax = b. Recently, the reweighted l₁ minimization and l₁ greedy algorithm have been introduced to improve the convergence of the l₁ minimization problem. As an extension, a generalized l₁ greedy algorithm for computerized tomography (CT) is proposed in this paper. It is implemented as a generalized total variation minimization for images with sparse gradients in CT. A numerical experiment is also given to illustrate the advantage of the new algorithm.