The advent of large language models (LLMs) has opened up new opportunities in the field of mobile task automation. Their superior language understanding and reasoning capabilities allow users to automate complex and repetitive tasks. However, due to the inherent unreliability and high operational cost of LLMs, their practical applicability is quite limited. To address these issues, this paper introduces MobileGPT1, an innovative LLM-based mobile task automator equipped with a human-like app memory. MobileGPT emulates the cognitive process of humans interacting with a mobile app---explore, select, derive, and recall. This approach allows for a more precise and efficient learning of a task's procedure by breaking it down into smaller, modular sub-tasks that can be re-used, re-arranged, and adapted for various objectives. We implement MobileGPT using online LLMs services (GPT-3.5 and GPT-4) and evaluate its performance on a dataset of 185 tasks across 18 mobile apps. The results indicate that MobileGPT can automate and learn new tasks with 82.7% accuracy, and is able to adapt them to different contexts with near perfect (98.75%) accuracy while reducing both latency and cost by 62.5% and 68.8%, respectively, compared to the GPT-4 powered baseline.