Radially polarized field under strong focusing has emerged as a powerful manner for fluorescence microscopy. However, the refractive index (RI) mismatch-induced aberrations seriously degrade imaging performance, especially under high numerical aperture (NA). Traditional adaptive optics (AO) method is limited by its tedious procedure. Here, we present a computational strategy that uses artificial neural networks to correct the aberrations induced by RI mismatch. There are no requirements for expensive hardware and complicated wavefront sensing in our framework when the deep network training is completed. The structural similarity index (SSIM) criteria and spatial frequency spectrum analysis demonstrate that our deep-learning-based method has a better performance compared to the widely used Richardson-Lucy (RL) deconvolution method at different imaging depth on simulation data. Additionally, the generalization of our trained network model is tested on new types of samples that are not present in the training procedure to further evaluate the utility of the network, and the performance is also superior to RL deconvolution.