FINGREEN3D is an open-source package for computation of the free-surface Green's function under a finite water depth, which is the core-part of the boundary integral equations in the potential flow theory for analysis of wave-structure interactions. It is currently written in FORTRAN 90. The code is based on a state-of-the-art method developed in recent years by the authors. The main strategy of this method is to use a set of different series expansions in appropriate sub-regions. Therefore, we can avoid calculating the Green's function by direct time-consuming integrations. FINGREEN3D is freely distributed under the LGPL License, Version 3.0, https://www.gnu.org/licenses/lgpl-3.0.html, and may be modified and extended by researchers who intend to enhance its capabilities and port the code to other platforms. The Mendeley release is the first(original) release of the FINGREEN3D package. The subsequent versions can be traced via its GitHub homepage: https://github.com/liuyingyi-ukyushu/FinGreen3D. Tutorials are given inside the FinGreen3D package. Instructions for compiling and running the tutorial program, as well as calling the FinGreen3D dynamic-link library from a user program, is well introduced in the Readme.txt file. FINGREEN3D is developed in the hope that it can contribute to the continuous development of offshore floating renewable energy systems as well as other ocean/marine engineering applications, regardless of academic or industrial purpose. Please cite the following associated paper in your relevant publications if the FINGREEN3D code or its executable (dynamic-link library) has contributed to your work: Yingyi Liu et al. A reliable open-source package for performance evaluation of floating renewable energy systems in coastal and offshore regions. Energy Conversion and management, 2018.