While Large language models (LLMs) have advanced natural language processing tasks, their growing computational and memory demands make deployment on resource-constrained devices like mobile phones increasingly challenging. In this paper, we propose SHARP (SHaring Adjacent Layers with Recovery Parameters), a novel approach to accelerate LLM inference by sharing parameters across adjacent layers, thus reducing memory load overhead, while introducing low-rank recovery parameters to maintain performance. Inspired by observations that consecutive layers have similar outputs, SHARP employs a two-stage recovery process: Single Layer Warmup (SLW), and Supervised Fine-Tuning (SFT). The SLW stage aligns the outputs of the shared layers using L_2 loss, providing a good initialization for the following SFT stage to further restore the model performance. Extensive experiments demonstrate that SHARP can recover the model's perplexity on various in-distribution tasks using no more than 50k fine-tuning data while reducing the number of stored MLP parameters by 38% to 65%. We also conduct several ablation studies of SHARP and show that replacing layers towards the later parts of the model yields better performance retention, and that different recovery parameterizations perform similarly when parameter counts are matched. Furthermore, SHARP saves 42.8% in model storage and reduces the total inference time by 42.2% compared to the original Llama2-7b model on mobile devices. Our results highlight SHARP as an efficient solution for reducing inference costs in deploying LLMs without the need for pretraining-scale resources.