High computational complexity is the bottleneck of the holographic display. Aiming at the problem, a new hologram coding and reconstruction algorithm based on compressed sensing theory and lensless Fourier transform is proposed. Lensless off-axis Fourier hologram is generated by computer, and then the hologram is sampled and reconstructed by the theory of compressed sensing. At last, the original image is reconstructed by the hologram. The advantage of this method is that only some useful sampling coefficients of the hologram is used to reconstruct the original image well, which solves the problem of large volume of sampling data of the sensor and achieves the goal of reduction of the computational complexity. Simulation results show that the correlation coefficient of reconstructed image with 20% compressive sampling rate is 0.85; when compressive sampling rate of hologram with 50%, the coefficient reaches 0.9999. In addition, a holographic reconstruction system is built to verify the hologram compression sampling theory. The experimental results indicate that the original image can be clearly reconstructed by the system, which proves the feasibility of the method.