Abstract: Alternating direction methods(ADM)are a class of the effective approaches for solving the convex optimization problems with linear constraint structure.Due to these algorithms can be used to solve the complex large－scale problem into several subproblems，it has attracted the attention of many optimization scholars at home and abroad，and has become particularly important in the field of image processing，compress sensing，physics and economics et al.However，without further special structures，it is excessively expensive to solve those realistic problems accurately.To address this issue，this paper considered a modified alternating direction method(MADM)to solve total variation problem，which could be viewed as an extension of the particular alternating direction method for minimizing total variation problem，called TVAL3.In the proposed method，a novel strategy for choice of the initial BB(Barzilai－Borwein)stepsize was introduced to improve the convergence speed and guarantee the stability of the algorithm.The modified initial BB stepsize effectively employed the information of the current point and the first two iteration points，which combineed the two gradient directions that was used in the steepest descent method(SD)and BB method.With the uses of the modified initial BB stepsize in the non－monotone line search technique，the approximate solution of subproblems was obtained，and the global convergence of the modified algorithm was also proved by extending existing theoretical results.Finally，in order to test the performance of the proposed algorithm，we applied it to solving problems in image reconstruction problem with total variation regularization under small scale，noiseless and large－scale，noisy.And by comparing MADM with TVAL3 in terms of running time，the number of iterations，the relative error and the effect of reconstruction，the numerical results demonstrate that the proposed method have much better performance in convergence speed and reconstruction effect.