Phase synchronization issue, that is caused by spotting gestures from video stream, varying frame-rates, speed of subject's implementation, should be overcome in developing Human-Computer Interaction (HCI) application using dynamic hand gestures. This paper tackles an interpolation technique to efficiently solve this issue. We firstly propose a new representation of dynamic hand gestures space that consists of both spatial and temporal features extracted from the hand gestures. The spatial features are extracted based on a manifold learning technique (ISOMAP) that takes into account non-linear features (e.g., poses of hand, illumination conditions, hand-shape differences). The temporal features handle hand movements thanks to Kanade-Lucas-Tomasi (KLT), good feature points tracking algorithm. We then propose an efficient interpolation scheme on the constructed space of hand gestures. This scheme ensures inter-period phase continuity as well as normalizes length of the hand gestures. We examine the proposed method with three different large datasets of dynamic hand gestures. Evaluation results confirm that the best accuracy rate achieves at 98% that is significantly higher than results from previous works (at 94%). The proposed method suggests a feasible and robust solution addressing technical issues in developing HCI application using the hand gestures to control home appliance devices.