This paper examines the challenge of Computed Tomography (CT) image reconstruction problem from incomplete projection data. Based on the underdetermined system of equations, we incorporate a Total Variation (TV) regularization term and data fidelity term to formulate a TV-CT model for image reconstruction. We present a comprehensive derivation of the primal-dual method to solve the corresponding saddle point problem, as well as the primal-dual algorithms. Particularly, we introduce adaptive stepsize strategies for the proposed primal-dual algorithm to enhance the reconstruction performance. Finally, numerical experiments are conducted to verify the proposed method, including comparisons with state-of-the-art methods.