We demonstrate single-shot nondiffracting light-sheet microscopy by the incoherent superposition of dispersed polychromatic light sources. We characterized our technique by generating a Bessel light-sheet with a supercontinuum light-source and a C-light-sheet using a diode laser, and demonstrated its applicability to fluorescence microscopy. We emphasize that our method is easily implementable and compatible with the requirements of high-resolution microscopy.