Cylindrical waveguides have a wide range of applications in photonic integrated circuits because of lower transmission losses. This paper proposes a directional coupler composed of a cylindrical silicon nanowire waveguide and a metal-based cylindrical hybrid plasmon waveguide. The coupling characteristics of the coupler are analyzed theoretically and are also simulated using the finite-difference time-domain method. The results show that the coupler can operate effectively with a relatively short coupling length, displaying low insertion loss, and a high coupling efficiency and extinction ratio. This study also shows how the TM mode in the plasmon waveguide can be excited with the TE mode of the dielectric waveguide. This directional coupler has a potential application in signal exchanging and mode switching between the dielectric and plasmon waveguides in photonic integrated circuits.