Biometric recognition technology based on eye-movement dynamics has been in development for more than ten years. Different visual tasks, feature extraction and feature recognition methods are proposed to improve the performance of eye movement biometric system. However, the correct identification and verification rates, especially in long-term experiments, as well as the effects of visual tasks and eye trackers' temporal and spatial resolution are still the foremost considerations in eye movement biometrics. With a focus on these issues, we proposed a new visual searching task for eye movement data collection and a new class of eye movement features for biometric recognition. In order to demonstrate the improvement of this visual searching task being used in eye movement biometrics, three other eye movement feature extraction methods were also tested on our eye movement datasets. Compared with the original results, all three methods yielded better results as expected. In addition, the biometric performance of these four feature extraction methods was also compared using the equal error rate (EER) and Rank-1 identification rate (Rank-1 IR), and the texture features introduced in this paper were ultimately shown to offer some advantages with regard to long-term stability and robustness over time and spatial precision. Finally, the results of different combinations of these methods with a score-level fusion method indicated that multi-biometric methods perform better in most cases.