Inefficient traffic signal control methods may cause numerous problems, such as traffic congestion and waste of energy. Reinforcement learning (RL) is a trending data-driven approach for adaptive traffic signal control in complex urban traffic networks. Although the development of deep neural networks (DNN) further enhances its learning capability, there are still some challenges in applying deep RLs to transportation networks with multiple signalized intersections, including non-stationarity environment, exploration-exploitation dilemma, multi-agent training schemes, continuous action spaces, etc. In order to address these issues, this paper first proposes a multi-agent deep deterministic policy gradient (MADDPG) method by extending the actor-critic policy gradient algorithms. MADDPG has a centralized learning and decentralized execution paradigm in which critics use additional information to streamline the training process, while actors act on their own local observations. The model is evaluated via simulation on the Simulation of Urban MObility (SUMO) platform. Model comparison results show the efficiency of the proposed algorithm in controlling traffic lights.