Recently, three-terminal synaptic devices have attracted considerable attention owing to their nondestructive weight-update behavior, which is attributed to the completely separated terminals for reading and writing. However, the structural limitations of these devices, such as a low array density and complex line design, are predicted to result in low processing speeds and high energy consumption of the entire system. Here, we propose a vertical three-terminal synapse featuring a remote weight update via ion gel, which is also extendable to a crossbar array structure. This synaptic device exhibits excellent synaptic characteristics, which are achieved via precise control of ion penetration onto the vertical channel through the weight-control terminal. Especially, the applicability of the developed vertical organic synapse array to neuromorphic computing is demonstrated using a simple crossbar synapse array. The proposed synaptic device technology is expected to be an important steppingstone to the development of high-performance and high-density neural networks.