The phase and amplitude of object light field can be simultaneously recorded by hologram, and all the depth cues required by human eyes can be provided by its reconstructed image. Therefore, holography is considered as an ideal true three-dimensional (3D) display technology. With the development of computer technology and electronic technology, computer-generated holography appears. The real and virtual scene can be recorded and reconstructed by Computer-Generated Hologram (CGH). It is more suitable for 3D display. However, the huge amount of computation is one of the bottlenecks to realize high-quality CGH based 3D display. Improving the computing speed is an important direction in the application research of CGH based 3D display. Layer-based algorithm is a critical approach to generate CGH. The three-dimensional object is divided into several parallel planes. Then, the complex amplitude diffracted by each layer of object onto the hologram plane is solved by Fast Fourier Transform (FFT). The complex amplitudes are superposed to form the complex amplitude of object light field on hologram plane. Finally, the hologram is obtained by interfering it with the reference light. The calculation speed is effectively improved, because FFT is used. However, the sample frequency of object plane and hologram plane is constrained by sampling theorem. The interpolation operation of data is adopted to archive this constraint. It reduces the calculation speed, especially when the aspect ratio of object plane or hologram plane is large. The mathematical model of Fresnel diffraction consists of integral term and coefficient term. The integral term of discrete object light field is a discrete-time Fourier transform, which is a periodic function. According to the theorem of digital signal processing, spatial interpolation leads to spatial frequency domain expansion and the spectrum is the periodic expansion of original one. Generally, a low-pass filter is used to filter the unexpected components. Fortunately, the human eye acts as a low-pass filter in 3D display. We can sample the object plane with human eye resolution and calculate one period of integral term. Then, obtain the integral term of hologram plane by periodic expansion. The computation amount of integral term is reduced. Moreover, the coefficient term can be decomposed into two independent parts: row coefficient and column coefficient. We can calculate one row and one column coefficients separately and then combine them into complete ones. The amount of calculation is further reduced. A novel fast algorithm is proposed to improve the computing speed of large size CGH, according to the characteristics of layer-based computer generated Fresnel hologram model. First, complete the following calculation for each layer. 1) Calculate the coefficients of row and column respectively. 2) Calculate a period of the integral term by using the FFT. 3) The calculated integral term is periodic expanded on the hologram plane, and the distribution of the diffraction field on the hologram plane is obtained by multiplying the integral term of each sample point and the coefficient which formed by the combination of the row and column coefficients of the sample. Then the diffraction fields of all layers are summed up and interfered with the reference beam to obtain the hologram. Experiments were carried out to verify the algorithm. Firstly, two holograms were generated by traditional algorithm and proposed one separately. The reconstructed images were compared. No difference was found. Secondly, the reconstructed images under three different viewing angles were taken by the camera. The occlusion relationship between the object and the background is correct. Continuous parallax changes can be seen when human eyes move. Thirdly, the reconstructed images at different distances were inspected. The depth information was reconstructed correctly. Fourthly, the relationship between reconstructed image quality and layer interval was inspected. When the layer interval meets the human eye resolution, the observed reconstructed image is continuous in each viewing angle. When the human eye resolution is not met, the layered reconstructed image is likely to appear in large angle tilt observation. Finally, the computing speed of different size of hologram was inspected. The experimental results show that the larger the hologram size is, the faster the proposed algorithm is. The number of layers has no effect on the speed improvement multiple of the proposed algorithm. When the sample point of volume is 1 174×1 174×41 points, and the hologram resolution is 11 700×11 700 pixels, the calculation speed of proposed algorithm is 13 times higher than that of traditional algorithm. In summary, the proposed algorithm not only ensures good reconstruction effect, but also significantly improves the computing speed of computer-generated Fresnel hologram. It has a good performance in the calculation of large-scale holograms. Further, after calculating one period of the integral term, the subsequent calculations are independent of each other. This makes it possible to further improve the computing speed of hologram by using parallel computing.