<p>Tikhonov regularization has been widely employed for solving the regularized solutions of linear discrete ill-posed problems, which are typically formulated as systems of linear algebraic equations or linear least squares problems involving a noisy right-hand side. Therefore, endeavors to mitigate the influence of the noise vector on an approximation generated by a certain iterative algorithm will enhance the quality of the regularization solution to some extent. This paper presents a novel randomized iterative algorithm comprising of two sub-procedures for the solution of Tikhonov regularization problem. The initial procedure employs the CGLS algorithm to modify the contaminated right-hand side vector, aiming to minimize the impact of noise. Following this, the second procedure utilizes the randomized Kaczmarz algorithm to solve the modified linear system of algebraic equations. The convergence rate of the proposed randomized iterative algorithm is theoretically analyzed and its effectiveness is experimentally validated through 2D tomography image reconstruction problems.</p>