The simple lens computational imaging method provides an alternative way to achieve high-quality photography. It simplifies the design of the optical-front-end to a single-convex-lens and delivers the correction of optical aberration to a dedicated computational restoring algorithm. Traditional single-convex-lens image restoration is based on optimization theory, which has some shortcomings in efficiency and efficacy. In this paper, we propose a novel Recursive Residual Groups network under Generative Adversarial Network framework (RRG-GAN) to generate a clear image from the aberrations-degraded blurry image. The RRG-GAN network includes dual attention module, selective kernel network module, and residual resizing module to make it more suitable for the non-uniform deblurring task. To validate the evaluation algorithm, we collect sharp/aberration-degraded datasets by CODE V simulation. To test the practical application performance, we built a display-capture lab setup and reconstruct a manual registering dataset. Relevant experimental comparisons and actual tests verify the effectiveness of our proposed method.