This paper presents the development of the core spreading vortex element method, a mesh-free method for simulating 3D viscous flow over bluff bodies. The developed method simulates external flow around complex geometry by tracking local velocities and vorticities of particles introduced within the fluid domain. The viscous effect is modeled using the core spreading method coupled with a splitting spatial adaption scheme and a smoothing interpolation scheme for overlapping issues and population control, respectively. The particle’s velocity is calculated using the Biot-Savart formulation. To accelerate computation, the fast multipole method (FMM) is employed. The solver was validated using a number of benchmark problems for both unbounded and bounded flows at low Reynolds numbers. For unbounded cases, simulation of the collision of two vortex rings was performed. The energy spectrum calculated using the current core spreading diffusion model approached that of the particle strength exchange model. To test the performance of the method in simulating bounded flow problems, simulation of flow around a sphere was carried out. The results were found to be in very good agreement with those reported in the literature.