This paper proposes a design of anisotropic metagratings with a polarization selective layer to enable anomalous wide-angle reflection with polarization conversion. The proposed structure consists of three layers including a pattern layer, a polarization selective layer, and a ground. The metagrating patterns are designed with a set of perpendicular electric dipoles, which exhibit independent control of transverse electric (TE) and transverse magnetic (TM) wave responses. In addition, the polarization selective layer is designed to be electromagnetically transparent for TE-polarized waves while enhancing efficiencies of beam steering and polarization conversion in TM-polarized waves. To validate the proposed design, two proof-of-concept metagrating samples are fabricated to exhibit dual and circular polarizations at 60° as the first-order diffraction mode, demonstrating their capability for diagonally-polarized normal incident waves. The results confirm that the proposed structure with the polarization selective layer plays a key role in achieving highly-efficient wide-angle reflection with polarization conversion functionality.