We demonstrate a single-photon sensitive spectrometer in the visible range, which allows us to perform time-resolved and multi-photon spectral correlation measurements at room temperature. It is based on a monochromator composed of two gratings, collimation optics, and an array of single photon avalanche diodes. The time resolution can reach 110 ps and the spectral resolution is 2 nm/pixel, limited by the design of the monochromator. This technique can easily be combined with commercial monochromators and can be useful for joint spectrum measurements of two photons emitted in the process of parametric down conversion, as well as time-resolved spectrum measurements in optical coherence tomography or medical physics applications.