We study the magnetism of a spin-1 substance Li2Ni2Mo3O12. The spin system consists of distorted honeycomb lattices and linear chains of Ni2+ spins. Li+ ions enter about 25% and 50% of the honeycomb and chain Ni sites, respectively, creating disorder in both spin subsystems. A magnetic phase transition occurs at Tc=8.0 K in the zero magnetic field. In low magnetic fields, the magnetization increases rapidly below Tc, decreases below 7 K, and finally becomes negative at low temperatures. We determine the magnetic structure using neutron-powder-diffraction results. The honeycomb lattices and linear chains show antiferromagnetic and ferromagnetic long-range order, respectively. We investigate static and dynamic magnetic properties using the local probe technique of muon spin relaxation. We discuss the origin of the negative magnetization.