Skyrmions can appear in non-centrosymmetric materials because of non-vanishing Dzyaloshinskii–Moriya interactions (DMIs). We investigate the magnetic properties of rhombohedral MX3 (M: V, Cr, Mn, Fe; X: Cl, Br, I) van der Waals materials with centrosymmetric lattices by combining first-principle calculations and Monte Carlo simulations. We determine that the Dzyaloshinskii–Moriya vector acting between the second nearest neighbor sites of the intralayer is non-zero and large in MX3, owing to the breaking of the local inversion symmetry. Large DMIs cause nanoscale magnetic vortices, i.e. that is, skyrmions. We observe both conventional skyrmions in CrCl3 and VCl3 and antiferromagnetic skyrmions in FeCl3 and merons in MnCl3. Furthermore, the skyrmions in CrCl3 and VCl3 have different helicities, indicating the possibility of controlling the helicity by electron/hole doping in MX3 materials. Van der Waals materials have high degrees of freedom in heterostructures and twisted structures, demonstrating promising potential as skyrmion materials.