The primal-dual hybrid gradient (PDHG) algorithm has been applied for solving linearly constrained convex problems. However, it ‎was ‎shown ‎that ‎without ‎some additional ‎assumptions, convergence may fail. ‎In ‎this ‎work, ‎we propose a new competitive prediction-correction primal-dual hybrid gradient algorithm to solve this kind of problem. Under some conditions, we prove the global convergence for the proposed algorithm with the rate of ‎$‎O(1/N)‎$ ‎in a nonergodic sense‎.‎ Comparative performance analysis of our proposed approach with other related methods on some matrix completion and wavelet-based image inpainting test problems shows the outperformance of our approach, in terms of iteration number and CPU time.