We investigate the process innovation and contracting decisions of a dynamic supply chain consisting of a supplier and a manufacturer, with the manufacturer possessing private information about her efficiency of process innovation. To overcome the potential adverse selection problem due to the asymmetric information, the supplier designs a menu of supply contracts that stipulates both the wholesale price and the purchasing quantity. We find that under information asymmetry, the supplier will optimally set a higher wholesale price but a lower purchasing quantity for the manufacturer with high innovation efficiency than that for the manufacturer with low innovation efficiency. As a consequence, the manufacturer with high innovation efficiency will significantly underinvest in innovation due to information asymmetry in addition to the impact of the double marginalization effect. Moreover, although a longer contract period tends to better motivate innovation, it can also magnify the influences of adverse selection on supply chain contracting, leading to a higher wholesale price for the manufacturer with high innovation efficiency.