Continual forgetting task aims to continuously remove multiple target knowledge subsets from pre-trained models while maintaining the integrity of remaining knowledge. Existing methods suffer from both incomplete forgetting of target knowledge and unintended forgetting of indistinguishable remaining knowledge. To address these challenges, we propose the forgetting knowledge localization and isolation for continual forgetting in pre-trained vision models which precisely forgets target knowledge while reducing over-forgetting of remaining knowledge. To achieve precise forgetting, we first propose the forgetting knowledge layer localization to explore layers in the model which are more related to forgetting knowledge. Then, we design the forgetting knowledge parameter isolation to isolate the parameters sensitive to forgetting knowledge in these selected layers, mitigating over-forgetting of remaining knowledge. Finally, we fine-tune these isolated parameters and freeze the remaining parameters to achieve efficient forgetting while maintaining high performance on retained datasets. Extensive experimental results demonstrate that our method achieves superior performance over state-of-the-art methods across multiple continual forgetting tasks. We will release the source codes and pre-trained models.