In this paper, we introduce an inertial parallel CQ subgradient extragradient method for nding a common solutions of variational inequality problems. The novelty of this paper is using linesearch methods to nd unknown L constant of L-Lipschitz continuous mappings. Strong convergence theorem has been proved under some suitable conditions in Hilbert spaces. Finally, we show applications to signal and image recovery, and show the good eciency of our proposed algorithm when the number of subproblems is increasing.