The present invention provides an anti-thrombogenic and cellular-adhesion coating composition for blood-contacting surfaces. The coating comprises a covalent complex of from 1 to 30 hydrophobic silyl moieties of Formula I: ##STR1## wherein R.sub.1 is an C.sub.1-18 alkyl or C.sub.6-32 aryl group, each R.sub.2 is independently selected from the group consisting of C.sub.1-18 alkyl and C.sub.6-32 aryl, R.sub.3 is N or O, n is a number from 1 to 10, directly bound to a heparin molecule via covalent bonding, with an adhesive molecule directly bound to the heparin molecule. In one embodiment, the coating comprises benzyl-(1,2 dimethyl)disilyl heparin, wherein an adhesive molecule, such as fibronectin, is bound to the heparin.