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Meta-reinforcement learning (meta-RL) is a promising approach that enables the agent to learn new tasks quickly. However, most meta-RL algorithms show poor generalization in multi-task scenarios due to the insufficient task information provided only by rewards. Language-conditioned meta-RL improves the generalization capability by matching language instructions with the agent's behaviors. While both behaviors and language instructions have symmetry, which can speed up human learning of new knowledge. Thus, combining symmetry and language instructions into meta-RL can help improve the algorithm's generalization and learning efficiency. We propose a dual-MDP meta-reinforcement learning method that enables learning new tasks efficiently with symmetrical behaviors and language instructions. We evaluate our method in multiple challenging manipulation tasks, and experimental results show that our method can greatly improve the generalization and learning efficiency of meta-reinforcement learning. Videos are available at https://tumi6robot.wixsite.com/symmetry/.