In this work, we propose a hybrid parallel Jaya optimisation algorithm for a multi-core environment with the aim of solving large-scale global optimisation problems. The proposed algorithm is called HHCPJaya, and combines the hyper-population approach with the hierarchical cooperation search mechanism. The HHCPJaya algorithm divides the population into many small subpopulations, each of which focuses on a distinct block of the original population dimensions. In the hyper-population approach, we increase the small subpopulations by assigning more than one subpopulation to each core, and each subpopulation evolves independently to enhance the explorative and exploitative nature of the population. We combine this hyper-population approach with the two-level hierarchical cooperative search scheme to find global solutions from all subpopulations. Furthermore, we incorporate an additional updating phase on the respective subpopulations based on global solutions, with the aim of further improving the convergence rate and the quality of solutions. Several experiments applying the proposed parallel algorithm in different settings prove that it demonstrates sufficient promise in terms of the quality of solutions and the convergence rate. Furthermore, a relatively small computational effort is required to solve complex and large-scale optimisation problems.