Mixture of Experts (MoE) architectures have recently advanced the scalability and adaptability of large language models (LLMs) for continual multimodal learning. However, efficiently extending these models to accommodate sequential tasks remains challenging. As new tasks arrive, naive model expansion leads to rapid parameter growth, while modifying shared routing components often causes catastrophic forgetting, undermining previously learned knowledge. To address these issues, we propose LLaVA-CMoE, a continual learning framework for LLMs that requires no replay data of previous tasks and ensures both parameter efficiency and robust knowledge retention. Our approach introduces a Probe-Guided Knowledge Extension mechanism, which uses probe experts to dynamically determine when and where new experts should be added, enabling adaptive and minimal parameter expansion tailored to task complexity. Furthermore, we present a Probabilistic Task Locator that assigns each task a dedicated, lightweight router. To handle the practical issue that task labels are unknown during inference, we leverage a VAE-based reconstruction strategy to identify the most suitable router by matching input distributions, allowing automatic and accurate expert allocation. This design mitigates routing conflicts and catastrophic forgetting, enabling robust continual learning without explicit task labels. Extensive experiments on the CoIN benchmark, covering eight diverse VQA tasks, demonstrate that LLaVA-CMoE delivers strong continual learning performance with a compact model size, significantly reducing forgetting and parameter overhead compared to prior methods. These results showcase the effectiveness and scalability of our approach for parameter-efficient continual learning in large language models. Our code will be open-sourced soon.