Multimodal point-of-interest (POI) recommendation seeks to enhance recommendation performance by leveraging diverse types of POI information, such as textual descriptions, user reviews, and images. Recently, Large Language Models (LLMs) have demonstrated remarkable capabilities in various recommendation tasks. However, to the best of our knowledge, there has been no prior work exploring the application of LLMs to multimodal POI recommendation. In this paper, we propose a novel method, i.e., LFT4POI, that incorporates LLM fine-tuning to effectively model and integrate multimodal POI data for improved recommendation performance. Specifically, LFT4POI introduces a multitask LLM fine-tuning framework for large language models, combining contrastive learning and supervision LLM fine-tuning to align the model with POI-specific contexts. After fine-tuning, the large language model generates enriched POI embeddings, which are fused with sequential patterns from a conventional POI recommendation model (e.g., MMPOI) for final recommendations. Experiments on NYC and TKY datasets demonstrate superior performance: our method outperforms seven baselines including MMPOI, STGCN, and STGN with an average 4% improvement across all the metrics such as Acc@20 and MRR. Ablation studies further confirm the contributions of each component, specifically multimodal fusion and LLM fine-tuning.