Instruction tuning constitutes a prevalent technique for tailoring Large Vision Language Models (LVLMs) to meet individual task requirements. To date, most of the existing approaches are confined to single-task adaptation, whereas the requirements in real-world scenarios are inherently varied and continually evolving. Thus an ideal LVLM should sustain continual instruction tuning in the face of stream-task distributions (i.e., different domains, emerging capabilities, and new datasets) while minimizing the forgetting of previously acquired knowledge. To achieve this, we propose a new benchmark for COntinuAl inStruction Tuning on LVLMs (COAST), which encompasses the aforementioned domain-incremental, capability-incremental, and dataset-incremental configurations. In terms of methodology, we propose Continual LLaVA, a rehearsal-free method tailored for continual instruction tuning in LVLMs. To circumvent the additional overhead associated with experience replay, we freeze LVLMs and construct the dual increment embeddings for each input instruction to facilitate parameter-efficient tuning. Specifically, the increment embeddings can be decomposed into two principal components: 1) intrinsic increment embeddings to encode task-specific characteristics. To achieve this, we set up a low-rank pool containing candidate embeddings, from which we select the relevant ones based on their similarity with the user instructions; 2) contextual increment embeddings to investigate the inter-dependencies across tasks. In this regard, the low-rank embeddings chosen in the previous tasks are aggregated via learnable weighted sum to provide complementary hints. Extensive experiments indicate that the proposed Continual LLaVA outperforms previous methods by significantly reducing the forgetting during the continual instruction tuning process.