Recommender systems have become essential tools for enhancing user experiences across various domains. While extensive research has been conducted on recommender systems for movies, music, and e-commerce, the rapidly growing and economically significant Non-Fungible Token (NFT) market remains underexplored. Recommender systems have the potential to significantly enhance user engagement, increase the time users spend on platforms, and deepen user involvement. Consequently, effective implementation of such systems could serve as a catalyst for invigorating the NFT market. However, the unique characteristics of the NFT market, such as the high sparsity of user–item interactions, anonymity of blockchain, and dual nature, present challenges not encountered in traditional recommender systems, highlighting the importance of developing tailored solutions to cater to its specific needs and unlock its full potential. In this paper, we examine the distinctive characteristics of NFTs and propose the first recommender system specifically designed to address NFT market challenges. In specific, we develop a Multi-Attention Recommender System for NFTs (NFT-MARS) with three key characteristics: (1) graph attention to handle sparse user–item interactions, (2) multi-modal attention to incorporate feature preference of users, and (3) multi-task learning to consider the dual nature of NFTs as both artwork and financial assets. We demonstrate the effectiveness of NFT-MARS compared to various baseline models using the actual transaction data of NFTs collected directly from the blockchain for four of the most popular NFT collections.