The present invention provides a liquid crystal composition obtained by dissolving a dichroic dye in a mixture of a cross-linked polymer having a liquid crystalline group in the side chains and a low molecular weight liquid crystal, and preferably the cross-linked polymer is a cross-linked siloxane polymer having a liquid crystalline group in the side chains, and the dielectric constant anisotropy of the liquid crystal composition is changed from positive to negative by increasing the frequency of the voltage to be applied. The present invention further provides a liquid crystal element containing the liquid crystal composition and a cross-linked siloxane polymer preferably usable for the liquid crystal composition.