Ghost imaging is a fascinating framework which constructs the image of an object by correlating measurements between received beams and reference beams, none of which carries the structure information of the object independently. Recently, by taking into account space-time duality in optics, computational temporal ghost imaging has attracted attentions. Here, we propose a novel Fourier temporal ghost imaging (FTGI) scheme to achieve single-shot non-reproducible temporal signals. By sinusoidal coded modulation, ghost images are obtained and recovered by applying Fourier transformation. For demonstration, non-repeating events are detected with single-shot exposure architecture. It's shown in results that the peak signal-to-noise ratio (PSNR) of FTGI is significantly better (13dB increase) than traditional temporal ghost imaging in the same condition. In addition, by using the obvious physical meaning of Fourier spectrum, we show some potential applications of FTGI, such as frequency division multiplexing demodulation in the visible light communications.