Due to its high molecular specificity, Raman spectroscopy is a well-established analytical tool. Usually the inelastically scattered Raman light is spectrally dispersed by a spectrometer. Here, we present an alternative method, using an optical fiber as dispersive element. As the group velocity within the fiber is wavelength-dependent, different Raman bands arrive at different times at the detector. In combination with time-correlated single-photon counting, Raman spectra can be measured in the time domain. As detector we implemented a Superconducting Nanowire Single-Photon Detector (SNSPD), which possesses a timing accuracy of about 20 ps. Within this contribution we show first results of Raman spectra measured in the time domain using gradient index fibers of varying length.