A polycaprolactone fumarate polymer useful as a matrix material for a biocompatible scaffold for tissue engineering applications is disclosed. The polycaprolactone fumarate polymer can be prepared by reacting caprolactone with an alkane polyol to prepare a polycaprolactone precursor, and then reacting the polycaprolactone precursor with fumaric acid or a salt thereof to prepare the polycaprolactone fumarate polymer. The use of an alkane diol, such as 1,2-propanediol, provides a linear polycaprolactone diol precursor. The use of an alkane triol, such as glycerol, provides a branched polycaprolactone triol precursor. The biocompatible polycaprolactone fumarate formulation releases no diethylene glycol or other undesirable byproducts during degradation.