In this paper, we present a modified subgradient extragradient method with double inertial extrapolation terms and a non-monotonic adaptive step size for solving quasi-monotone and Lipschitz continuous variational inequalities in real Hilbert spaces. Under some suitable conditions, we obtain the weak convergence theorem of our proposed algorithm. Moreover, strong convergence is obtained when the cost operator is strongly pseudo-monotone and Lipschitz continuous. Finally, several numerical results illustrate the effectiveness and competitiveness of our algorithm.