Multi-task model merging offers a promising paradigm for integrating multiple expert models into a unified system without additional training. Existing state-of-the-art techniques, such as Task Arithmetic and its variants, merge models by accumulating task vectors—defined as the parameter differences between pre-trained and fine-tuned models. However, task vector accumulation is often hindered by knowledge conflicts, where conflicting components across different task vectors can lead to performance degradation during the merging process. To address this challenge, we propose Conflict-Aware Task Merging (CAT Merging), a novel training-free framework that selectively trims conflict-prone components from the task vectors. CAT Merging introduces several parameter-specific strategies, including projection for linear weights and masking for scaling and shifting parameters in normalization layers. Extensive experiments on vision and vision-language tasks demonstrate that CAT Merging effectively suppresses knowledge conflicts, achieving average accuracy improvements of up to 4.7% (ViT-B/32) and 2.0% (ViT-L/14) over state-of-the-art methods.