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We demonstrate twisted nematic liquid crystal (LC) polarization gratings (TNPGs) with a high first-order diffraction efficiency (>90%) that have the twist angle as constant, whereas the azimuthal angle of the mid-plane liquid-crystal director varies linearly in space. The high diffraction-efficiency design scheme is derived by means of the Jones matrix method. The designed first-order diffraction efficiency theoretically reaches 100% for the thick LC layer in which the retardation equals (n + 1/2)λ (n is an integer and λ is the wavelength). We also present a simple model for the grating period- and twist angle-dependent threshold voltage of the Freedericksz transition in TNPGs.