The structure of multi-domain micromagnetic states in hcp cobalt nanoparticles of spheroidal shape has been studied using numerical simulation in the range of diameters 20–200 nm. The single-domain diameters of the particles are determined depending on their aspect ratio. The complicated vortex structure of domain walls for two- and three-domain micromagnetic configurations is investigated. It has been shown that three domain states are actually strongly deformed two vortex states. In hcp cobalt particles of sufficiently large sizes two types of three-domain micromagnetic states with close total energies have been obtained. They differ in different magnetization directions of the exchange cores of the vortex domain walls. The remanent magnetization of particles has been calculated for two- and three-domain micromagnetic states. The single-domain diameters of fcc cobalt nanoparticles with cubic type of magnetic anisotropy were also calculated.