Continuum percolation in particle systems underlies a wide spectrum of material properties. Previous studies on the percolation phenomena of 2D particle systems focused on the random packing of some simple particles including circles, ellipses, rectangles, etc. In this work, the geometrical model of superellipses which can capture more of essential features of particle shapes from rhombuses via ellipses to rectangles is introduced and an efficient algorithm for detecting the collision of these particles is proposed then. By using finite-size scaling technique, the global percolation thresholds phi(c) for homogeneous systems comprising congruent superellipses with aspect ratio a/b in [0.1,10.0] and shape parameter m in [0.5, +infinity) are explored and the effect of particle characteristic on the values of phi(c) is quantified by an approximately numerical formula. Afterwards, the algorithm of particle percolation is extended to the heterogeneous systems consisting of the binary superellipses with different a/b or m. The dependence of percolation threshold phi(c) for these particulate systems on the number fraction lambda of the particles is further studied briefly. The results reveal that phi(c) is closely related to the aspect ratio a/b and parameter m for all the superellipse systems. Besides, for the heterogeneous systems comprising the binary superellipses, the value of phi(c) is not only dependent on the number fraction of these adopted particles but also the specific thresholds of the homogeneous systems comprising the corresponding particles. (C) 2019 Elsevier B.V. All rights reserved.