The quality of the reconstructed holographic three-dimensional image is seriously influenced by the noise. A novel encoded algorithm combining the Burch code with the four-step phase shifting method is presented to remove the noise and improve the contrast and resolution of the reconstructed image. The reconstructed three-dimensional images are compared with the results of the median filtering. The performance parameters of two methods are analyzed. The experimental results show that the zero-order light spot, conjugate image and speckle noise are suppressed effectively. The quality of the reconstructed image is noticeably improved.