Non-Fungible Tokens (NFTs) have recently received immense popularity in the digital art industry. An NFT represents ownership of a unique item that is stored on the blockchain and cannot be changed, replaced, and copied. The current NFT ecosystem falls short in trust features and is prone to illegitimate users, threats, and vulnerabilities. In this paper, we propose a blockchain-based solution for the NFT ecosystem that incorporates registration of the participating actors, involves a decentralized reputation system, provides incentives to its users through rewards, and penalizes misconduct. Our system design is built to ensure trust and credibility in the NFT ecosystem. The proposed solution leverages blockchain's intrinsic security features such as transparency, tamper-proof logs, data integrity, accountability, and non-repudiation. We use the decentralized storage of the InterPlanetary File System (IPFS) to store the NFTs' metadata, whereas their hash is stored on the chain. We present algorithms along with their implementation, testing, and validation details. We demonstrate how our solution, as well as smart contract code, is secure enough against common security threats and attacks. We make our smart contract code publicly available on the GitHub repository.