The ability to use eye movement signals as a feature in biometric recognition is a novel characteristic of biometric recognition technology. However, present technologies have not fully exploited the correlation features between eye movement signals. To address this, we propose an eye movement biometric recognition model that is based on recurrence plot encoding and the InceptionV3 model. We first encode the original eye movement signal using the recurrence plot to obtain a 2-D image that is then used as input for the InceptionV3 model to perform biometric recognition. Our experimental results using the GazeBaseV2.0 eye movement dataset demonstrate that our proposed model achieved a high biometric recognition accuracy of 96.58% ± 0.66% using the recurrence plot transformation of the horizontal gaze position signals and the InceptionV3 model, surpassing the accuracy achieved by other models. The use of horizontal gaze position eye movement signals for biometric recognition outperforms the use of vertical gaze position signals when using our proposed methods. Furthermore, the biometric recognition that is achieved through recurrent plot encoding is superior to that achieved using Markov transition fields and Gramian angular field transformations.