The invention provides an optical fractional order Fourier transform device based on a transform material and a design method, which belongs to the field of transform materials and optical fractionalorder Fourier transform signal processing. The device mainly enlarges an input surface based on a traditional GRIN lens, and keeps an output surface unchanged or shrunk. The transformation relation with the traditional GRIN lens is acquired through a conformal transformation and other methods, and then a material transformation method is used to acquire the conformal transformation device of the refractive index of the device. The method comprises the steps that 1 the lens output surface and the lens thickness are unchanged on the basis of the traditional GRIN lens, and the bending angle of the lens is between 0 degree and 360 degrees; 2 the output surface of the lens is kept unchanged, and the lens is stretched to isotropy of each point; and 3 the material transformation method is used tocalculate the material parameters of the device. The device has the advantages of low measurement error and high resolution when a low-frequency chirp signal is input. The device is made of an isotropic material, which is good for engineering preparation.