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The on-ramp merging driving scenario is challenging for achieving the highest-level autonomous driving. Current research using reinforcement learning methods to address the on-ramp merging problem of automated vehicles (AVs) is mainly designed for a single AV, treating other vehicles as part of the environment. This paper proposes a control framework for cooperative on-ramp merging of multiple AVs based on multi-agent deep reinforcement learning (MADRL). This framework facilitates AVs on the ramp and adjacent mainline to learn a coordinate control policy for their longitudinal and lateral motions based on the environment observations. Unlike the hierarchical architecture, this paper integrates decision and control into a unified optimal control problem to solve an on-ramp merging strategy through MADRL.