The efficiency of metaheuristic algorithms depends significantly on the number of fitness value evaluations performed on candidate solutions. In addition to various intelligent techniques used to obtain better results, parallelization of calculations can substantially improve the solutions in cases where the problem is NP-hard and requires many evaluations. This study proposes a new parallel tabu search method for solving the Maximum Vertex Weight Clique Problem (MVWCP) on the Non-Uniform Memory Access (NUMA) architectures using the OpenMP parallel programming paradigm. Achieving scalability in the NUMA architectures presents significant challenges due to the high complexity of their memory systems, which can lead to performance loss. However, our proposed Tabu-NUMA algorithm provides up to (Formula presented.) speed-up with 64 cores for ten basic problem instances in DIMACS-W and BHOSLIB-W benchmarks. And it improves the performance of the serial Multi Neighborhood Tabu Search (MN/TS) algorithm for 38 problem instances in DIMACS-W and BHOSLIB-W benchmarks. We further evaluate our algorithm on larger datasets with thousands of edges and vertices from Network Data Repository benchmark problem instances, and we report significant improvements in terms of speed up. Our results confirm that the Tabu-NUMA algorithm is among the best recent algorithms for solving MVWCP on the NUMA architectures.