While reasoning technology like Chain of Thought (CoT) has been widely adopted in Vision Language Action (VLA) models, it demonstrates promising capabilities in end to end autonomous driving. However, recent efforts to integrate CoT reasoning often fall short in simple scenarios, introducing unnecessary computational overhead without improving decision quality. To address this, we propose AdaThinkDrive, a novel VLA framework with a dual mode reasoning mechanism inspired by fast and slow thinking. First, our framework is pretrained on large scale autonomous driving (AD) scenarios using both question answering (QA) and trajectory datasets to acquire world knowledge and driving commonsense. During supervised fine tuning (SFT), we introduce a two mode dataset, fast answering (w/o CoT) and slow thinking (with CoT), enabling the model to distinguish between scenarios that require reasoning. Furthermore, an Adaptive Think Reward strategy is proposed in conjunction with the Group Relative Policy Optimization (GRPO), which rewards the model for selectively applying CoT by comparing trajectory quality across different reasoning modes. Extensive experiments on the Navsim benchmark show that AdaThinkDrive achieves a PDMS of 90.3, surpassing the best vision only baseline by 1.7 points. Moreover, ablations show that AdaThinkDrive surpasses both the never Think and always Think baselines, improving PDMS by 2.0 and 1.4, respectively. It also reduces inference time by 14% compared to the always Think baseline, demonstrating its ability to balance accuracy and efficiency through adaptive reasoning.