Large language models (LLMs) have demonstrated considerable proficiency in general natural language processing (NLP) tasks. Instruction tuning, a successful paradigm, enhances the ability of LLMs to follow natural language instructions and exhibit robust generalization across general tasks. However, these models often encounter performance limitations across multiple tasks due to constrained model capacity. Expanding this capacity during the instruction tuning phase poses significant challenges. To address this issue, we introduce parameter-efficient sparsity crafting (PESC), which crafts dense models into sparse models using the mixture-of-experts (MoE) architecture. PESC integrates adapters into the MoE layers of sparse models, differentiating experts without altering the individual weights within these layers. This method significantly reduces computational costs and GPU memory requirements, facilitating model capacity expansion through a minimal parameter increase when guaranteeing the quality of approximation in function space compared to original sparse upcycling. Our empirical evaluation demonstrates the effectiveness of the PESC method. Using PESC during instruction tuning, our best sparse model outperforms other sparse and dense models and exhibits superior general capabilities compared to GPT-3.5. Our code is available at https://github.com/wuhy68/Parameter-Efficient-MoE.