Multi-lingual fine-tuning (MLF), which fine-tunes a multi-lingual language model (MLLM) with multiple source languages, aims to gain good zero-shot performance on target languages. In MLF, the fine-tuned model tends to fit the source languages while forgetting its cross-lingual knowledge obtained from the pre-training stage. This forgetting phenomenon degenerates the zero-shot performance of MLF, which remains under-explored. To fill this gap, this paper proposes a multi-lingual fine-tuning method, dubbed Less-forgetting Multi-lingual Fine-tuning (LF-MLF). In LF-MLF, we cast multi-lingual fine-tuning as a constrained optimization problem, where the optimization objective is to minimize forgetting, and constraints are reducing the fine-tuning loss. The proposed method has superior zero-shot performance; furthermore, it can achieve the Pareto stationarity. Extensive experiments on Named Entity Recognition, Question Answering and Natural Language Inference back up our theoretical analysis and validate the superiority of our proposals.