Flying-focal-spot (FFS) technique has been used for improving the sampling condition in advanced clinical CT by collecting multiple cone-beam data sets with the focal-spot at different locations at each "projection view". It has been demonstrated that the increased sampling rate in FFS scans can substantially reduce aliasing artifacts in reconstructed images. However, the increase of the sampling density through multiple illuminations at each view can result in the increase of radiation dose to the imaged subject. In this work, we have applied a compressive-sensing (CS)-based algorithm to image reconstruction from data acquired in FFS scans. The results of the study demonstrate that aliasing artifacts observed images reconstructed by use of analytic algorithms can be suppressed effectively in images reconstructed with this CS-based algorithm from only data acquired at one FFS scan.