Fourier series (FS) is an efficient tool for describing irregular geometries and has been employed to develop the FS-based particle model in the discrete element method (DEM). This work is devoted to extending the previous FS-based particle model to the Minkowski and Gilbert–Johnson–Keerthi (GJK)-based contact detection and resolution framework for DEM, and thus to improving its computational efficiency and compatibility with other conventional particle models. In the new FS-based particle model, instead of representing particle surface, the FS is proposed to represent the support function of particle surface. Particle surface and support points are then formulated based on the FS support function. As the Minkowski- and GJK-based detection and resolution framework relies heavily on the convexity of particles, the convexity constraint and the approach to generate convexity preserving FS-based particles are also presented. The accuracy of the new FS-based particle model for shape representation is analyzed using a set of irregular shape templates. DEM simulation of random packing and biaxial compression test with various particle models is also performed to demonstrate the computational performance and numerical stability of the new FS-based particle model.