This paper presents a GPU-based parallel implementation of the Enhanced Jaya (EJAYA) algorithm for solving large-scale systems of nonlinear equations. EJAYA is a gradient-free metaheuristic optimization scheme based on the population-based parameter-less Jaya algorithm that has recently been shown to be capable of solving nonlinear equation systems, a class of challenging problems that are difficult to solve by traditional approaches, particularly as systems become larger. The proposed parallel algorithm was implemented using the Julia programming language on a high-performance GeForce RTX 3090 GPU with 10 496 CUDA cores and 24 GB GDDR6X VRAM and was tested using a set of difficult scalable nonlinear equation system problems. The obtained results, with average speedups up to 122.25x, evidenced the capability of the proposed GPU-based parallel algorithm to meet the computational demands of the important class of problems under consideration.