The polytopal element has proven highly valuable in the numerical simulation of various engineering challenges, thanks to its remarkable flexibility in mesh generation. However, constructing shape functions for arbitrary polytopal elements remains a challenging task. In boundary element methods (BEM), the domain integral is transformed into a boundary integral using the fundamental solution of the governing equation—this makes mesh generation in BEM notably simple and efficient. Nevertheless, BEM typically requires solving systems of equations with dense matrices, which can lead to high computational costs when dealing with large-scale problems. In this work, we aim to bring together the strengths of the fundamental solution and the polytopal element by introducing a new numerical approach: the Fundamental Solution-based Virtual Element Method (FS-VEM). Inspired by the virtual element method, we employ a projection technique that effectively avoids the need to explicitly define internal shape functions within polytopal elements. As a result, only the degrees of freedom located on the element boundaries need to be considered, greatly simplifying the formulation. Moreover, the fundamental solution is incorporated into the projection equations to convert domain integrals into boundary integrals. We have applied the proposed FS-VEM to solve heat conduction and wave propagation problems, and several numerical examples are presented to illustrate its performance. The results demonstrate that FS-VEM achieves high accuracy, which can be further improved by either increasing the number of elements or refining the number of nodes along element boundaries. We believe this method offers a promising direction for future developments in numerical simulation.