This paper proposes lossless linear predictive coding based on the directionality of the interference patterns of a hologram. We approached this study from two aspects. First, to determine the directionality of the interference patterns, we performed differential pulse coding modulation (DPCM), segmenting interference patterns into n blocks and scanning the pixels in eight directions for each block. Then, we determined the direction that had minimum entropy, calculating entropy in each direction, and encoded the difference by DPCM in the determined direction. In the second approach, we attempted linear prediction using the prediction coefficients for the determined direction based on the first process. In this case, the DPCM was utilized only to determine the direction in which to progress prediction about the original pixel. Then, we calculated the difference between the predicted and the original, and encoded it. Through the above procedure, we derived an appropriate compression scheme for the hologram by comparing DPCM with the linear predictive coding. Experimental results showed that the compression rate of 26.7% could be obtained through the first process.