Conventional 2D touch-based interaction methods for handheld Augmented Reality (AR) cannot provide intuitive 3D interaction due to a lack of natural gesture input with real-time depth information. The goal of this research is to develop a natural interaction technique for manipulating virtual objects in 3D space on handheld AR devices. We present a novel method that is based on identifying the positions and movements of the user's fingertips, and mapping these gestures onto corresponding manipulations of the virtual objects in the AR scene. We conducted a user study to evaluate this method by comparing it with a common touch-based interface under different AR scenarios. The results indicate that although our method takes longer time, it is more natural and enjoyable to use.