The target of a coreference resolution system is to cluster all mentions that refer to the same entity in a given context. All coreference resolution systems need to solve two subtasks; one task is to detect all of the potential mentions, and the other is to learn the linking of an antecedent for each possible mention. In this paper, we propose an actor-critic-based neural coreference resolution system, which can achieve both mention detection and mention clustering by leveraging an actor-critic deep reinforcement learning technique and a joint training algorithm. We experiment on the BERT model to generate different input span representations. Our model with the BERT span representation achieves the state-of-the-art performance among the models on the CoNLL-2012 Shared Task English Test Set.