Abstract: Smart meters with real-time, high-sampling rate, and high-precision capabilities lay a data foundation for multi-user electricity load forecasting. Currently, user-level load forecasting still faces challenges such as data privacy leakage, insufficient data samples, and weak model generalization ability. Traditional federated learning methods derive a global model with common characteristics across multiple clients through collaborative training. However, these models overlook the differences in electricity consumption patterns and data distributions among diverse users. Additionally, synchronous aggregation is susceptible to device disconnection and network latency issues. To address these issues, an asynchronous personalized federated learning (Async-PFL) method is proposed. Based on this, a hybrid CNN-GRU model is designed for short-term load forecasting. The Async-PFL enhances the adaptability of the predictive model to heterogeneous data from different users through a two-stage personalization method based on model layering and local fine-tuning, thereby making the model better suited to the individual characteristics of diverse users. The asynchronous federated aggregation algorithm, combined with a lag-tolerant model distribution and a time-lag weight function, effectively mitigates the negative impact of node loss and network delays on global model updates, thereby accelerating model convergence. The proposed method is experimentally validated on the "Building Data Genome Project 2" dataset. The results demonstrate that the proposed method not only protects privacy but also outperforms single models and standard federated learning in terms of both model accuracy and system robustness.