Molecule-based electrorheological (ER) materials as a novel type of ER materials, the inclusion compound [$H_2$($eta$-CD-A)-PTA] between p-toluenesulfonic acid (PTA, guest) and $H_2$($eta$-CD-A) (host) that is dicarboxylic acid of $eta$-cyclodextrin ($eta$-CD), and the rare earth (RE) complexes [($eta$-CD-A)-PTA]$_3RE_2$ (RE=La, Gd, Y) of $H_2$($eta$-CD-A)-PTA, were synthesized. The ER performance and dielectric property of the materials were studied. Our results show that the molecule-based ER materials assembled using $eta$-cyclodextrin as a substrate, especially the inclusion compound and its rare earth (RE) complexes exhibit clear ER effect. The inclusion PTA can markedly enhance the ER performance of $H_2$($eta$-CD-A) material. The ER activity of the yttrium complex is the highest among these materials. The characteristic of the molecule in molecule-based ER materials is an important factor in influencing ER property.