Holographic data storage (HDS) utilizes the unique properties of light for writing and reading two-dimensional (2D) data from holographic media, providing significantly higher densities and faster data transfer rates than traditional storage media for short-term dependencies. With its ability to store terabytes of data in a single crystal, HDS has garnered attention as a promising candidate for next-generation storage technologies. However, the 2D interference caused by hologram dispersion during the reading process poses a significant obstacle to achieving reliable and efficient HDS systems. This study proposes a method for enhancing the accuracy of estimating the 2D intersymbol interference (ISI) using a recurrent neural network (RNN) equalizer for HDS systems. The proposed method leverages the ability of RNNs to model complex and temporal dependencies in data and more accurately estimate the interference caused by ISI and interchannel interference (ICI) in HDS systems. In addition, to recreate the relationship between the samples in the training process, RNN is applied to fields such as computer vision, natural language process, speech recognition, and so on. We evaluated the performance of our proposed method on a simulation model of HDS system and compared it with the previous studies. In the simulations, the proposed method outperformed the previous schemes in terms of bit error rate, indicating its potential for improving the reliability and efficiency of HDS systems.