Giant zero-field cooling exchange-bias-like behavior with H EB = 3.49kOe was found in an antiperovskite Mn3Co0.61Mn0.39N compound. The magnetic structure of Mn3Co0.61Mn0.39N was resolved to be ferrimagentic ordering composed of canted Γ5g antiferromagnetic (AFM) and ferromagnetic (FM) along the [111] direction by the neutron diffraction technique. The exchange coupling model was proposed together with the first principles calculation for further understanding this exchange-bias-like behavior. It was found that the ferromagnetic exchange interaction between FM and the canted Γ5g AFM play an important role in the particular exchange-bias-like behavior. The exchange coupling constructed in the lattice is distinct from the interactions between collinear AFM and FM in conventional exchange bias system. In addition to the enhanced horizontal shift, hysteresis loops obtained after FC cooling also exhibited vertical shift. The macroscopic vertical shift of the magnetization is ascribed to the increase of the magnetic moment of canted Γ5g spins along the external magnetic field. This finding will promote the development of advanced magnetic devices.