The Max-Cut problem consists of finding a partition of the graph nodes into two subsets, such that the sum of the edge weights having endpoints in different subsets is maximized. This NP-hard problem for non planar graphs has different applications in areas such as VLSI and ASIC design. This paper proposes an evolutionary hybrid algorithm based on low-level hybridization between Memetic Algorithms and Variable Neighborhood Search. This algorithm is tested and compared with the results, found in the bibliography, obtained by other hybrid metaheuristics for the same problem. Achieved experimental results show the suitability of the approach, and that the proposed hybrid evolutionary algorithm finds near-optimal solutions. Moreover, on a set of standard test problems, new best known solutions were produced for several instances.