The hemocompatible material has a strong and tight synthetic substrate to which a biological animal tissue such as animal e.g. bovine, pericardium, is adhered by dispersing a substrate constituting material in a solvent. The substrate is made of elastomer such as polyurethane or silicone elastomer. The tissue is treated for several days using a glycol such as polyethyleneglycol, once adhered on the substrate. An independent claim is also included for a method for fabricating a hemocompatible material.