<p>In this paper, we introduce a low-cost double inertial projection algorithm with a generalized step-size rule for solving variational inequality problems in real Hilbert spaces. A key feature of our method is that the projections in each iteration are performed onto moving balls. Since projecting onto a ball has an explicit expression, our algorithm is easy to implement. Unlike many existing methods that project onto half-spaces containing the feasible set, our approach uses balls entirely contained within the feasible region, ensuring that every projection remains feasible. We establish strong convergence of the algorithm under the assumption that the operator is pseudo-monotone. Finally, we present several numerical examples to illustrate the effectiveness of our approach on several complex problems.</p>