A cover structure of an internal combustion engine of a motorcycle includes an engine that is mounted on a motorcycle and includes a cooling device for cooling the engine. The cover structure includes a sprocket cover portion that covers from the width direction of the vehicle. The cover structure also includes a pipe cover portion that covers from the width direction of vehicle a discharge side hose and an intake side hose of the cooling device. The cover structure further includes a side surface cover that includes a joining portion which is vertically arranged from the sprocket cover portion towards the pipe cover portion so as to be in parallel with the discharge side hose. The intake side hose is arranged side by side in the width direction of the vehicle and integrally joins the sprocket cover portion with the pipe cover portion.