Manipulating the directional movement of liquid droplets is of significance for design and fabrication of some microHuidic devices. An energy-based method is adopted to analyse the directional movement of a droplet deposited in a conical tube or on a conical fibre. We perform an experiment to investigate the directional motion of a droplet in an open conical tube. Our theoretical analysis and experimental observations both demonstrate that surface tension can drive the droplet to move in the conical tube. The critical condition of the liquid moving in the conical tube is presented. We also analyse a droplet on a conical hydrophilic fibre, which can move from the thinner to the thicker end.