Abstract: The mathematical model of the hyperbolic cylinder transmission grating was established. The complex amplitude transmittance was derived from the definition of an optical path when a parallel light passes through a singular hyperbolic cylinder. The expression of light intensity distribution for a hyperbolic cylinder transmission grating on the frequency plane was obtained by means of Fourier transform method. The variation of diffractive light intensity distribution with the hyperbola semi-real axis were simulated with MATLAB. The diffraction fringe agrees with the result of theoretical analysis. The potential application of the hyperbolic cylinder transmission grating in the field of optics is pointed out.