Most interactive user interfaces (UIs) for virtual reality (VR) applications are based on the traditional eye-centred UI design principle, which primarily considers the user's visual searching efficiency and comfort, but the hand operation performance and ergonomics are relatively less considered. As a result, the hand interaction in VR is often criticized as being less efficient and precise. In this paper, the user's arm movement features, such as the choice of the hand being used and hand interaction position, are hypothesized to influence the interaction results derived from a VR study. To verify this, we conducted a free hand target selection experiment with 24 participants. The results showed that (a) the hand choice had a significant effect on the target selection results: for a left hand interaction, the targets located in spaces to the left were selected more efficiently and accurately than those in spaces to the right; however, in a right hand interaction, the result was reversed, and (b) the free hand interactions at lower positions were more efficient and accurate than those at higher positions. Based on the above findings, this paper proposes a hand-adaptive UI technique to improve free hand interaction performance in VR. A comprehensive comparison between the hand-adaptive UI and traditional eye-centred UI was also conducted. It was shown that the hand-adaptive UI resulted in a higher interaction efficiency and a lower physical exertion and perceived task difficulty than the traditional UI.