Recent advances in large language models have demonstrated that Supervised Fine-Tuning (SFT) with Chain-of-Thought (CoT) reasoning data distilled from large reasoning models (e.g., DeepSeek R1) can effectively transfer reasoning capabilities to non-reasoning models. However, models fine-tuned with this approach inherit the "overthinking" problem from teacher models, producing verbose and redundant reasoning chains during inference. To address this challenge, we propose \textbf{L}ong-\textbf{S}hort Chain-of-Thought \textbf{Mixture} \textbf{S}upervised \textbf{F}ine-\textbf{T}uning (\textbf{LS-Mixture SFT}), which combines long CoT reasoning dataset with their short counterparts obtained through structure-preserved rewriting. Our experiments demonstrate that models trained using the LS-Mixture SFT method, compared to those trained with direct SFT, achieved an average accuracy improvement of 2.3\% across various benchmarks while substantially reducing model response length by approximately 47.61\%. This work offers an approach to endow non-reasoning models with reasoning capabilities through supervised fine-tuning while avoiding the inherent overthinking problems inherited from teacher models, thereby enabling efficient reasoning in the fine-tuned models.