An intravenous lead for use with a cardiac device for implantation in the coronary venous system of the heart includes a lead body that is adapted to be routed through the vascular system into the coronary sinus with the distal end portion of the lead placed in the great cardiac vein or branch vein. The lead body includes a fixation member disposed just proximal of its tip. The fixation member comprises a radially expandable polymeric matrix that incorporates an osmotic agent so that when placed in a aqueous medium it will swell. Thus, when placed in a cardiac vein, the swelling of the fixation member will anchor the lead against longitudinal displacement due to body motion, blood flow and the beating action of the heart.