Light-element compounds hold great promise of high critical temperature superconductivity judging from the theoretical perspective. A hydrogen-rich material, benzene, is such a kind of candidate but also an organic compound. A series of first-principles calculations are performed on the electronic structures, dynamics properties, and electron-phonon interactions of solid benzene at high pressures. Benzene is found to be dynamically stable in the pressure range of 180-200 GPa and to exhibit superconductivity with a maximum transition temperature of 20 K at 195 GPa. The phonon modes of carbon atoms are identified to mainly contribute to the electron-phonon interactions driving this superconductivity. The predicted superconductivity in this simplest pristine hydrocarbon shows a common feature in aromatic hydrocarbons and also makes it a bridge to organic and hydrogen-rich superconductors.