First-principles calculations are performed to investigate the magnetic characteristics in the tripotassium doped picene, especially for the effects induced by the volume variations. When changing volume, both crystal lattice constants and atomic positions are optimized. For the system with the experimental crystal volume, the doped picene shows a weak antiferromagnetic instability. When the volume expands from this experimental crystal volume, the antiferromagnetic spin ordering becomes clear. The electronic structures show that the magnetism comes from the spin unbalance on the π orbitals of the C atoms. On the contrary, both ferromagnetic and antiferromagnetic spin orderings are strongly suppressed as the volume is reduced. Our results indicate that the magnetism is sensitive to the variation of volume or pressure in the tripotassium doped picene. No metal-insulator transition is observed for several considered volumes.