ABSTRACT Using all the data of the High Energy X-ray Timing Experiment (HEXTE) on board the Rossi X-ray Timing Explorer for Scorpius X-1 from 1996 February to 2012 January, we systematically search for hard X-ray tails in the X-ray spectra in 20–220 keV and, together with the data of the Proportional Counter Array (PCA), investigate the evolution of the detected hard X-ray tails along the Z-track on its hardness-intensity diagram (HID). The hard X-ray tails are detected in 30 observations and their presence is not confined to a specific position on the HID. Our analysis suggests that from the horizontal branch (HB), through the normal branch (NB), to the flaring branch (FB) on the HID, the hard X-ray tail becomes hard and its flux decreases. Jointly fitting the PCA+HEXTE spectra in 3–220 keV, it is found that the Bulk-Motion Comptonization (BMC) could be an alternative mechanism for producing the hard X-ray tails on the HB and the NB of this source. The temperature of the seed photons for the BMC spans in the range of ∼(2.4–2.6) keV, indicating that the seed photons might come from the surface of the neutron star (NS) or the boundary layer and, therefore, the BMC process could take place around the NS or in the boundary layer. Some possible mechanisms for producing the hard X-ray tails on the FB are given.