The geometry, spin multiplicity, magnetic moment, electronic density of states and the spin density of single-layer trigonal graphene quantum dots with zigzag edges have been systematically investigated using density functional theory with the generalized gradient approximation under different sizes. The calculated results such as lattice constants are in good agreement with experimental data and indicate that the system behaves like metal, while the electrons with up spins occupy the Fermi energy. The influence of quantum size effect is remarkable in the system of small size. It is also found that the sp2 hybridization and nonbonding electrons play an important part in the single-layer trigonal graphene quantum dots, just like in graphene. The spin multiplicity and magnetic moment of the system increase with the increase of the system size. Based on our calculation, the total magnetic moment of the system mainly comes from the nonbonding electrons on the 2p orbital of the zigzag boundary. Our calculation may be helpful in designing devices based on trigonal graphene quantum dots.