Developing metal-free electrocatalysts is vitally significant for oxygen molecule dissociation. Graphdiynes (GDY) doped with nonmetal atoms are designed and optimized as metal-free electrocatalysts, and their oxygen molecule dissociation catalytic performances are evaluated by density functional theory. The results of formation energies and cohesive energies reveal that the most favorable site for B, Si, P, S, As, Se and Te doping is the sp(2)-C atom at benzene ring (X-b), the most preferred sites for N and O doping is the sp-C atom nearest benzene ring at the chain (X-1 GDY). The O-2 molecules are chemisorbed on B, N, O, Si, P, S-doped GDYs, the O-O bonds increase from 1.23 angstrom to 1.39-1.57 angstrom. But, the O-2 dissociation activation barrier on B, O, Si, P, S-doped GDY monolayers is up to 1.31-4.01 eV, indicating that this reaction is difficult to occur at room temperature. The O-2 is physisorbed on As, Se and Te-doped GDY monolayers with a distance between O-2 and GDY planes of 2.40-2.77 angstrom. The N-doped GDY has a small dissociation activation barrier of 0.90 eV, which may be a metal-free catalyst. The calculations promote further application of heteroatom doped GDYs on oxygen reduction reaction and other reactions.