Perovskite colloidal quantum dots (CQDs) enable a solution-processed approach toward lasers, simultaneously providing tunable wavelength, high quantum efficiency, large absorption cross-section, and long Auger lifetimes. However, broad-band single-mode lasers based on such CQDs have been proven to be challenging. Here we report broad-band single-mode lasers from solution-processed CsPbX3 (X = Cl, Br, I) CQDs based on a high-quality zinc oxide microrod hexagonal whispering-gallery microcavity. A typical single-mode laser with ultra-narrow linewidth (B0.21 nm, quality factor B3000) at 11.7 mJ cm_2 was obtained at 636 nm based on the conformal deposition of CsPb(Br0.5I0.5)3 CQDs on an individual hexagonal zinc oxide microrod cavity with a radius of about B776 nm. Moreover, by tuning the halogen ratio, synthesis temperature and the size of the zinc oxide microrods, broad-band tunable single-mode lasers are obtained across the entire visible spectrum from 417 nm to 723 nm. These results represent a significant step towards easy solution-processed broad-band tunable single-mode lasers.