The emergence of harvesting robotics offers a promising solution to the issue of limited agricultural labor resources and the increasing demand for fruits. Despite notable advancements in the field of harvesting robotics, the utilization of such technology in orchards is still limited. The key challenge is to improve operational efficiency. Taking into account inner-arm conflicts, couplings of DoFs, and dynamic tasks, we propose a task planning strategy for a harvesting robot with four arms in this paper. The proposed method employs a Markov game framework to formulate the four-arm robotic harvesting task, which avoids the computational complexity of solving an NP-hard scheduling problem. Furthermore, a multi-agent reinforcement learning (MARL) structure with a fully centralized collaboration protocol is used to train a MARL-based task planning network. Several simulations and orchard experiments are conducted to validate the effectiveness of the proposed method for a multi-arm harvesting robot in comparison with the existing method.