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Brain-inspired Hyperdimensional (HD) computing is an emerging technique for cognitive tasks in the field of low-power design. As a fast-learning and energy-efficient computational paradigm, HD computing has shown great success in many real-world applications. However, an HD model incrementally trained on multiple tasks suffers from the negative impacts of catastrophic forgetting. The model forgets the knowledge learned from previous tasks and only focuses on the current one. To the best of our knowledge, no study has been conducted to investigate the feasibility of applying multi-task learning to HD computing. In this paper, we propose Task-Projected Hyperdimensional Computing (TP-HDC) to make the HD model simultaneously support multiple tasks by exploiting the redundant dimensionality in the hyperspace. To mitigate the interferences between different tasks, we project each task into a separate subspace for learning. Compared with the baseline method, our approach efficiently utilizes the unused capacity in the hyperspace and shows a 12.8% improvement in averaged accuracy with negligible memory overhead.