To take full advantage of rapidly deployable unmanned aerial vehicles (UAVs), it is essential to effectively compose many UAV images into one observation image over a region of interest. In this paper, we propose fast image mosaicking using a triangulated irregular network (TIN) constructed from tiepoints. We conduct pairwise tiepoint extraction and rigorous bundle adjustment to generate rigorous tiepoints. We apply a bucketing algorithm to the tiepoints and generate evenly distributed tiepoints. We then construct a TIN from the bucketed tiepoints and extract seamlines for image stitching based on the TIN. Image mosaicking is completed by mapping UAV images along the seamlines onto a reference plane. The experimental results showed that the image mosaicking based on a TIN of bucketed tiepoints could produce image mosaics with stable and fast performance. We expect that our method could be used for rapid image mosaicking.