A parallel Jaya algorithm implemented on the graphics processing unit (GPU-Jaya) is proposed to estimate parameters of the Li-ion battery model in this paper. Similar to the generic Jaya algorithm (G-Jaya), the GPU-Jaya is free of tuning algorithm-specific parameters. Compared with the G-Jaya algorithm, three main procedures of the GPU-Jaya, the solution update, fitness value computation, and the best/worst solution selection are all computed in parallel on GPU via a compute unified device architecture (CUDA). Two types of memories of CUDA, the global memory and the shared memory are utilized in the execution. The effectiveness of the proposed GPU-Jaya algorithm in estimating model parameters of two Li-ion batteries is validated via real experiments while its high efficiency is demonstrated by comparing with the G-Jaya and other considered benchmarking algorithms. The experimental results reflect that the GPU-Jaya algorithm can accurately estimate battery model parameters while tremendously reduce the execution time using both entry-level and professional GPUs.