In this article, we use the so-called $\eta$-approximation method for solving a new class of nonconvex variational problems with exponential $(p; r)$-invex functionals. In this approach, we construct $\eta$-approximated variational problem and $\eta$-approximated Mond- Weir dual variational problem for the considered variational problem and its Mond-Weir dual variational problem. Then several duality results for considered variational problem and its Mond-Weir dual variational problem are proved by the help of duality results established between $\eta$-approximated variational problems mentioned above.