Eye state prediction is the process of determining whether the users' eyes are in opened or closed state. It has been widely employed in human computer interaction, brain-computer interfaces, etc. In this paper, we investigated the classification performances of different distance metrics and number of neighbour parameters on the problem of predicting eye states. We conducted experiments on real-world EEG Eye State Data set which is intended to find appropriate approaches for eye state prediction. The classification performances were evaluated for accuracy measurement using the ten-fold leave-one-out cross-validation. The results demonstrate that the distance metrics and number of neighbour parameters highly affect the performance. Compared to previous works, the following two points were improved: (i) not only the euclidean distance but also other distance metrics' performances were investigated for EEG based eye state prediction and (ii) better classification accuracy rates were achieved compared to previous k-NN based studies.