Ghost imaging allows image reconstruction by correlation measurements between a light beam that interacts with the object without spatially resolved detection and a spatially resolved light beam that never interacts with the object. The two light beams are copies of each other. Its computational version removes the requirement of a spatially resolved detector when the light intensity pattern is pre-known. Here, we exploit the temporal analogue of computational ghost imaging, and demonstrate a computational distributed fiber-optic sensing technique. Temporal images containing spatially distributed scattering information used for sensing purposes are retrieved through correlating the "integrated" backscattered light and the pre-known binary patterns. The sampling rate required for our technique is inversely proportional to the total time duration of a binary sequence, so that it can be significantly reduced compared to that of the traditional methods. Our experiments demonstrate a 3 orders of magnitude reduction in the sampling rate, offering great simplification and cost reduction in the distributed fiber-optic sensors.