Metaverse and Digital Twin (DT) have attracted much academic and industrial attraction to approach the future digital world. This paper introduces the advantages of deep reinforcement learning (DRL) in assisting Metaverse system-based Digital Twin. In this system, we assume that it includes several Metaverse User devices collecting data from the real world to transfer it into the virtual world, a Metaverse Virtual Access Point (MVAP) undertaking the processing of data, and an edge computing server that receives the offloading data from the MVAP. The proposed model works under a dynamic environment with various parameters changing over time. The experiment results show that our proposed DRL algorithm is suitable for offloading tasks to ensure the promptness of DT in a dynamic environment.