Variational inequality problems have a wide range of applications in economics and finance transportation mathematical planning mechanics and other fields. In recent years the problem of variational inequalities has been studied by many scholars and these studies have mainly focused on solving monotone or pseudo-monotone variational inequalities. This article presented an algorithm for solving non-monotone variational inequality problems in real Hilbert spaces. A modified inertial subgradient extragradient algorithm with Armijo linear search was constructed using the inertia principle and Mann-type method. Under the assumption of non-Lipschitz continuity it was proved that the sequence of iterations generated by the algorithm converged strongly to the solution of the variational inequality problems. It is worth noting that the proof of the theorem does not require any monotonicity assumption for the mapping. Finally two numerical experiments were given to illustrate the effectiveness and superiority of the algorithm in the paper. The results obtained extend and improve many recent results.