We developed a planar-type graphene-based plasmonic photodetector (PD) for the development of all-graphene photonic-integrated-circuits (PICs). By configuring the graphene plasmonic waveguide and PD structure all-in-one, the proposed graphene PD detects horizontally incident light. The photocurrent profile with opposite polarity is the maximum at graphene-electrode interfaces due to a Schottky-like barrier effect at the interface. The photocurrent amplitude increases with an increase of the graphene-metal interface length. Obtaining time constants of less than 39.7 ms for the time response, we concluded that the proposed graphene PD could be exploited further for application in all graphene-based PICs.