Due to the interference of complex noise in holographic channels and the limitation of phase retrieve algorithms, the reliability of phase-modulated holographic data storage (PHDS) is seriously threatened, especially for multi-level phase modulation. A method for improving data reliability of PHDS is proposed by applying lossless data compression and low-density parity-check (LDPC) codes, which can eliminate data redundancy and correct errors effectively. We allocate the space saved by compression to store more LDPC parity bits and develop a method to determine the LDPC code rate and a method to manage the free space. Our method does not require the characteristics of the reconstructed phase distribution, which simplifies the statistical analysis and calculation. Simulation and experimental results demonstrate that our method greatly decreases the bit error rate (BER) and decoding iterations, and boosts the decoding success probability. For instance, when the phase error rate is 0.029 and the compression rate is 0.6, our method reduces the BER by 87.8%, the decoding iterations by 84.3%, and improves the decoding success probability by 93%. Our method enhances both data reliability and storage efficiency in PHDS.