Multi-wavelength (or multi-frequency) coherent light sources are essential for diverse applications. Nevertheless, regulating the multiple emission wavelengths in an ultra-compact scale is challenging. In this work, we demonstrate a novel topological nano-rainbow laser by exploiting topological synthetic dimensions in parameter space as a freedom to manipulate the optical resonances in a photonic crystal gain system. The system has spectrally isolated and spatially dispersed topological synthetic modes with near-diffraction-limited mode volumes and appropriately-designed high quality factors. We achieve high-performance nano-rainbow lasing with low threshold, broadband spectrum, large spontaneous emission factor (β), and milliwatt output power, simultaneously. These emission features are predetermined by the ultra-small mode volumes and appropriately-designed high quality factors of the spectrally and spatially isolated topological synthetic modes. This work enables high-performance, spatially multiplexed multi-wavelength emission for on-chip photonics, facilitating advances in broadband signal processing, optical computing, and beyond.