Abstract: Alternating direction method plays an important role in solving structured monotone variational inequality problems .In this paper ,we propose a modified projection alternating direction method by con‐structing a new descent direction ,w hich improves and promotes the projection alternating direction meth‐od given by Sun ,M. et al. Compared with Sun's method ,the proposed method has greater speed of con‐vergence and fewer iterations .Under the same assumptions ,we prove the global convergence property of the method ,and then test its effectiveness with a numerical example .