User modeling in large e-commerce platforms aims to optimize user experiences by incorporating various customer activities. Traditional models targeting a single task often focus on specific business metrics, neglecting the comprehensive user behavior, and thus limiting their effectiveness. To develop more generalized user representations, some existing work adopts Multi-task Learning (MTL)approaches. But they all face the challenges of optimization imbalance and inefficiency in adapting to new tasks. Continual Learning (CL), which allows models to learn new tasks incrementally and independently, has emerged as a solution to MTL's limitations. However, CL faces the challenge of catastrophic forgetting, where previously learned knowledge is lost when the model is learning the new task. Inspired by the success of prompt tuning in Pretrained Language Models (PLMs), we propose PCL, a Prompt-based Continual Learning framework for user modeling, which utilizes position-wise prompts as external memory for each task, preserving knowledge and mitigating catastrophic forgetting. Additionally, we design contextual prompts to capture and leverage inter-task relationships during prompt tuning. We conduct extensive experiments on real-world datasets to demonstrate PCL's effectiveness.