Backward and forward interpolations on a Fourier grid are computationally expensive operations for radio interferometric imaging algorithms. By merging these operations, we propose the Grid to Grid (G2G) method which aims to reduce the computational cost and memory footprint. We have also shown that the oversampling factor used for the convolution function in the G2G method strongly impacted the accuracy and computational speed. Acceleration on graphics processing units (GPU), well suited for this embarrassingly parallel algorithm, has been studied mainly for backward operation. Thus, we propose a GPU and CPU implementation of the G2G method on Nvidia A100 and Intel Ice Lake processors. Experiments have shown a GPU performance improvement with a Fourier-point throughput better than up to 37% regarding standard gridder and degridder.