<p>In this article, we propose a new modified projection and contraction algorithm for approximating solutions of a variational inequality problem involving a quasi-monotone and Lipschitz continuous mapping in real Hilbert spaces. We incorporate the technique of two-step inertia into a single projection and contraction method and prove a <i>weak</i> convergence theorem for the proposed algorithm. Our weak convergence theorem requires neither the prior knowledge of the Lipschitz constant nor the weak sequential continuity of the associated mapping. Under additional strong pseudomonotonicity, the <i>R</i>-linear convergence rate of the two-step inertial algorithm is derived. Finally, some numerical examples are given to illustrate the effectiveness and competitiveness of the proposed algorithm in comparison with some existing algorithms in the literature.</p>