The singlet plenoptic camera, which consists of a single lens, microlens array (MLA) and image sensor, possesses the superiority that the imaging system is compact and lightweight, which is beneficial to miniaturization. However, such plenoptic cameras suffer from severe optical aberrations and their imaging quality is inferior for post-capture processing. Therefore, this paper proposes an optical-aberrations-corrected light field re-projection method to obtain high-quality singlet plenoptic imaging. First, optical aberrations are modeled by Seidel polynomials and included into point spread function (PSF) modeling. The modeled PSF is subsequently used to reconstruct imaging object information. Finally, the reconstructed imaging object information is re-projected back to the plenoptic imaging plane to obtain high-quality plenoptic images without optical aberrations. PSF modeling is validated by a self-built singlet plenoptic camera and the utility of the proposed optical-aberrations-corrected light field re-projection method is verified by numerical simulations and real imaging experiments.