Organopolysiloxane polymer having a glycerol derivative which can swell up by containing at least its own weight of liquid oil obtained by the addition polymerization of the glycerol derivative having an alkenyl group expressed by the following general formula (b1) with the organohydrogen polysiloxane expressed by the following general formula (a2) (a2): R1dHeSiO(4-d-e)/2 (b1): R3fG1wherein R1 is a substituted or unsubstituted monovalent hydrocarbon group having 1 - 30 carbon atoms which does not contain an alkenyl group, G is polyglycerol, R3 is an alkenyl group having 2-20 carbon atoms, d and e are respectively defined by: 1.0 = d = 2.3, 0.001 = e = 1.0, 1.5 = d + e = 2.6, f is an integer from 2-10.
