Large language models (LLMs) exhibit remarkable capabilities in natural language processing but face catastrophic forgetting when learning new tasks, where adaptation to a new domain leads to a substantial decline in performance on previous tasks. In this paper, we propose Controlled LoRA (CLoRA), a subspace regularization method on LoRA structure. Aiming to reduce the scale of output change while introducing minimal constraint on model capacity, CLoRA imposes constraints on the direction of updating matrix’s null space. Experimental results on one-stage LLM finetuning tasks and continual learning settings highlight the superiority of CLoRA as an effective parameter-efficient finetuning method with catastrophic forgetting mitigating. Further investigation for model parameters indicates that CLoRA effectively balances the trade-off between model capacity and degree of forgetting. The code for implementing CLoRA will be publicly available.