As a transmission grating, a surface-relief (SR) grating with sawtooth shaped ridges and volume phase holographic (VPH) grating are widely used for instruments of astronomical observations. However the SR grating is difficult to achieve high diffraction efficiency at high angular dispersion, and the VPH grating has low diffraction efficiency in high diffraction orders. We propose novel gratings that solve these problems. We introduce the hybrid grism which combines a high refractive index prism with a replicated transmission grating, which has sawtooth shaped ridges of an acute apex angle. The birefringence VPH (B-VPH) grating which contains an anisotropic medium, such as a liquid crystal, achieves diffraction efficiency up to 100% at the first diffraction order for natural polarization and for circular polarization. The quasi-Bragg (QB) grating which consists of long rectangular mirrors aligned in parallel precisely, like a window blind, achieves diffraction efficiency of 60% or more in higher than the 4th diffraction order. The volume binary (VB) grating with narrow grooves also achieves diffraction efficiency of 60% or more in higher than the 6th diffraction order. The reflector facet transmission (RFT) grating which is a SR grating with sawtooth shaped ridges of an acute apex angle achieves diffraction efficiency up to 80% in higher than the 4th diffraction order.