A plant is grown or regenerated while suppressing the propagation of bacteria and fungi, by use of a carrier comprising a culture medium and a polymer constituting a network structure wherein the culture medium is substantially absorbed into and retained by the network structure in a proportion of 10% to 100% of the equilibrium culture medium absorption of the polymer constituting the network structure. The propagation of bacteria and fungi is much faster, and the metabolic rate thereof is much larger, than those of a plant. Therefore, the necessity of providing a nutrient (such as water and saccharide) from the culture medium to the bacteria and fungi is much greater than that in the plant tissue. Unlike a liquid medium, the culture medium which has been absorbed in the network structure comprising the polymer is hardly available to the bacteria and fungi, which have high metabolic activity. On the other hand, like a liquid medium, such a culture medium is available to a plant tissue having a low metabolic activity. The propagation of bacteria and fungi is effectively substantially suppressed without affecting the growth or regeneration of the plant.