Model-based meta-reinforcement learning (RL) methods have recently shown to be a promising approach to improving the sample efficiency of RL in multi-task settings. However, the theoretical understanding of those methods is yet to be established, and there is currently no theoretical guarantee of their performance in a real-world environment. In this paper, we analyze the performance guarantee of model-based meta-RL methods by extending the theorems proposed by Janner et al. (2019). On the basis of our theoretical results, we propose Meta-Model-Based Meta-Policy Optimization (M3PO), a model-based meta-RL method with a performance guarantee. We demonstrate that M3PO outperforms existing meta-RL methods in continuous-control benchmarks.