Most existing multi-agent reinforcement learning (MARL) methods are limited in the scale of problems they can handle. Particularly, with the increase of the number of agents, their training costs grow exponentially. In this paper, we address this limitation by introducing a scalable MARL method called Distributed multi-Agent Reinforcement Learning with One-hop Neighbors (DARL1N). DARL1N is an off-policy actor-critic method that breaks the curse of dimensionality by decoupling the global interactions among agents and restricting information exchanges to one-hop neighbors. Each agent optimizes its action value and policy functions over a one-hop neighborhood, significantly reducing the learning complexity, yet maintaining expressiveness by training with varying numbers and states of neighbors. This structure allows us to formulate a distributed learning framework to further speed up the training procedure. Comparisons with state-of-the-art MARL methods show that DARL1N significantly reduces training time without sacrificing policy quality and is scalable as the number of agents increases.