In goal-oriented dialogue tasks, the main challenge is to steer the interaction towards a given goal within a limited number of turns. Existing approaches either rely on elaborate prompt engineering, whose effectiveness is heavily dependent on human experience, or integrate policy networks and pre-trained policy models, which are usually difficult to adapt to new dialogue scenarios and costly to train. Therefore, in this paper, we present Nested Rollout Policy Adaptation for Goal-oriented Dialogue (NRPA-GD), a novel dialogue policy planning method that completely avoids specific model training by utilizing a Large Language Model~(LLM) to simulate behaviors of user and system at the same time. Specifically, NRPA-GD constructs a complete evaluation mechanism for dialogue trajectories and employs an optimization framework of nested Monte Carlo simulation and policy self-adaptation to dynamically adjust policies during the dialogue process. The experimental results on four typical goal-oriented dialogue datasets show that NRPA-GD outperforms both existing prompt engineering and specifically pre-trained model-based methods. Impressively, NRPA-GD surpasses ChatGPT and pre-trained policy models with only a 0.6-billion-parameter LLM. The proposed approach further demonstrates the advantages and novelty of employing planning methods on LLMs to solve practical planning tasks.