Holographic data storage (HDS) has attracted much attention as a next-generation storage medium. Because HDS suffers from two-dimensional (2D) inter-symbol interference (ISI), the partial-response maximum-likelihood (PRML) method has been studied to reduce 2D ISI. However, the PRML method has various drawbacks. To solve the problems, we propose a modified decision feedback equalizer (DFE) for HDS. To prevent the error propagation problem, which is a typical problem in DFEs, we also propose a reliability factor for HDS. Various simulations were executed to analyze the performance of the proposed methods. The proposed methods showed fast processing speed after training, superior bit error rate performance, and consistency.