Animal tissue has an extended history of clinical use in applications like heart valve bioprosthesis devices, cardiovascular surgical applications etc. but often does not last long after implantation in the body due to rapid unwanted degradation. The goal of this work is to develop novel composite biomaterials by grafting biological tissue with synthetic, biodegradable polymers. In the current research phase, porcine submucosa, ureter and bovine pericardial tissue are grafted with poly DL-lactide (PLA), poly glycolide (PGA) and poly DL-lactide glycolide (PLGA) copolymers. The grafted and control tissues are characterized by FTIR and SEM. The biodegradability of the tissue-graft composite materials is determined by pepsin and collagenase digestion assays, showing it can be tailored by varying the grafted polymer type and amount. The grafted tissues can be tuned for a particular clinical or tissue engineering applications including drug delivery with little or no burst release and sustained/controlled delivery.