The invention discloses a debris-flow drainage canal with energy dissipation and drainage functions and an application of the debris-flow drainage canal with energy dissipation and drainage functions. The drainage canal comprises a fully-lining drainage canal bottom plate and drainage canal side walls on two sides of the drainage canal bottom plate; the drainage canal bottom plate is in the shape of continuously-connected multiple-stage steps, the steps are provided with grooves; the width of the grooves on the top surfaces of the steps increases gradually along the flow direction of the debris flow, and the width of the grooves on the vertical surfaces of the steps decreases gradually; and the maximum width of the grooves on the top surfaces of the steps coincide with the maximum width B on the vertical surfaces of the steps. Compared wit the prior art, the step shape design is adopted to dissipate the energy of the debris flow all the way and the groove design is adopted to drain the debris flow, so the debris-flow drainage canal disclosed by the invention has high efficiency and good drainage capacity. By adjusting the height and the length of the steps and the size and the shape of grooves, the debris-flow drainagedrainage canal can be used for preventing the debris flow with any gradient and any nature.