Accurate　prediction　of　human　motion　is　essential　to　ensure　the　efficiency　and　safety　of　human-robot　interaction　(HRI),　especially　when　humans　and　robots　interact　closely　in　a　shared　environment.　A　novel　method　is　developed　in　this　work　to　address　three　fundamental　problems　in　human　arm　motion　prediction,　i.e.　given　the　early-stage　fingertip　trajectory　of　a　human　arm　reaching　motion,　how　to　predict　the　motion　duration,　the　motion　destination,　and　the　remaining　fingertip　trajectory.　First,　a　modified　minimum　jerk　model　(MMJM),　containing　three　input　parameters-the　motion　duration,　the　motion　destination,　and　the　early-stage　fingertip　trajectory,　is　developed　to　express　and　predict　the　remaining　fingertip　trajectory.　Next,　these　unknown　parameters　are　determined　by　determining　the　optimal　starting　time　of　motion　prediction　and　employing　Gaussian　process　regression　models　(GPRs).　Finally,　the　proposed　human　arm　motion　prediction　method　is　validated　by　simulations　and　HRI　experiments.