Event cameras offer promising properties, such as high temporal resolution and high dynamic range. These benefits have been utilized into many machine vision tasks, especially optical flow estimation. Currently, most existing event-based works use deep learning to estimate optical flow. However, their networks have not fully exploited prior hidden states and motion flows. Additionally, their supervision strategy has not fully leveraged the geometric constraints of event data to unlock the potential of networks. In this paper, we propose EV-MGRFlowNet, an unsupervised event-based optical flow estimation pipeline with motion-guided recurrent networks using a hybrid motion-compensation loss. First, we propose a feature-enhanced recurrent encoder network (FERE-Net) which fully utilizes prior hidden states to obtain multi-level motion features. Then, we propose a flow-guided decoder network (FGD-Net) to integrate prior motion flows. Finally, we design a hybrid motion-compensation loss (HMC-Loss) to strengthen geometric constraints for the more accurate alignment of events. Experimental results show that our method outperforms the current state-of-the-art (SOTA) method on the MVSEC dataset, with an average reduction of approximately 22.71% in average endpoint error (AEE). To our knowledge, our method ranks first among unsupervised learning-based methods.