The distinct discharge characteristics of an atmospheric-pressure cold plasma jet are investigated by using the temporal evolution of optical images and the discharge/substrate current. In a tubetype helium plasma jet reactor composed of a central high-voltage capillary electrode in a quartz tube and a ring-shaped ground electrode, plasma jet exhibits three discharge types, and the particular discharge type determines the variations in the discharge/substrate current and the relevant spatial characteristics of a jet. In order to find operation criteria to minimize substrate current induced material damage, we suggest diagrams of the discharge type and maximum substrate current in terms of the control parameters.