We have developed a filterless multicolor detection unit for fluorescence correlation spectroscopy (FCS). This grating-based setup is continuously tunable for multicolor separation and is thus a powerful alternative to the classical cascade of dichroic mirrors and filters. Our tailored platform allows for accommodation of up to 15 detection channels covering the entire visible spectral range. As a proof of principle, we successfully demonstrate simultaneous FCS of four distinct fluorescent quantum dot species being mixed in aqueous solution. Grating-based detection allows for spectral high-resolution FCS in a stable and compact setup and is a feasible tool for quantitative investigation of complex biomolecular dynamics on a single molecule level.