Abstract: For the convex optimization task generated in radio interference imaging, an improved convex optimization algorithm for radio interference imaging is proposed. Building on the highly parallelizable structure of the ADMM algorithm, a novel influence measure by taking into account correlation of front-back iterative solution is proposed, the weight solution in the forward (gradient) step of algorithm, to improve the accuracy of each reconstruction in each iteration. The design introduces a second-weighted update for solution in the forward (gradient) step of ADMM. The update equation depends on the two previous estimates, rather than only on the previous one. The improved algorithm not only can maintain parallel implementation structure and the same computational burden as ADMM, but also can achieve better reconstruction of noisy images. The simulations show that the proposed approach outperforms state-of-the-art imaging methods, both in terms of SNR and visual quality.